TL;DR;
- Faked image
- Not bin Laden
- Much less interesting than it seems
First Image: Rumsfeld and Hussein
Donald Rumsfeld's visit to Baghdad in 1983 is described in Wikipedia.

source unknown, allegedly 1983
A meeting between Rumsfeld and Hussein did take place in 1983 but the alleged photo of Rumsfeld+Hussein is almost certainly not a true record of that encounter. Iraqi TV coverage shows Hussein in army uniform. The (then secret) reports of the meeting describe Hussein as being in army uniform. Personally I think Photoshop may have been involved here, look at the "shadow" round Hussein's head, consider Rumsfeld's true appearance in 1983 and 2011.
Hussein elsewhere elsewhen
Rumsfeld in 2011
Rumsfeld in 1983
There is a declassified report Rumsfeld mission: December 20 meeting with Iraqi President Saddam Hussein on Rumsfeld's visit which describes the matters discussed by Donald Rumsfeld and Saddam Hussein. I assume the report is genuine and that the National Security Archive have reproduced it faithfully.
The Archive's summary is
At a 90-minute meeting with Donald Rumsfeld, Saddam Hussein evinces "obvious pleasure" at a letter Rumsfeld brought from President Ronald Reagan. The two discuss common U.S.-Iraqi interests, including Lebanon, Palestine, opposition to an outcome of the Iran-Iraq war that "weakened Iraq's role or enhanced interests and ambitions of Iran," and U.S. efforts to cut off arms sales to Iran. Rumsfeld says that the U.S. feels extremely strongly about terrorism and says that it has a home - in Iran, Syria, and Libya, and that it is supported by the Soviet Union. He encourages arrangements that might provide alternative transshipment routes for Iraq's oil, including pipelines through Saudi Arabia or to the Gulf of Aqaba in Jordan. The State Department calls the meeting a "positive milestone."
If you read the full text, there was clearly an exchange of views on a large number of regional issues but no mention (that I can see) of any new strong alliance between the USA and Iraq.
Conclusion (re image 1)
This faked photograph does not represent the forging of a strong alliance between Rumsfeld and Hussein or between the USA and Iraq.
In 1983 there was a slight thawing in diplomatic relations due to shared national interests in opposing Syrian and Israeli invasion of Lebanon, Iranian expansion etc.
Second image: Brzezinski and unnamed Pakistani army major
The second picture is one of a series available from the
Corbis Agency

© Bettmann/CORBIS
The caption there is
Original caption:Kyber Pass, Pakistan: United States Security Adviser Zbigniew Brzezinski looks into Afghanistan through the sights of a machine gun at a Pakistan Army outpost here on the border 2/3. Brzezinski toured the area and then continued talks with the Pakistan delegation in regards to an aid package.
Stock Photo ID: U1993539-24
Date Photographed: 03 February 1980
Model Released: No Release
Property Released: No Release
Location: Pakistan
Credit: © Bettmann/CORBIS
Licence Type: Rights Managed (RM)
It seems questionable whether Osama bin-Laden would have been present in a Pakistani border post in 1980 in the uniform of a major in the Pakistani army and employed to hand weapons to visiting dignitaries.
This is well covered in 911 Myths which identifies an article in the Washington Post on February 4, 1980, which says
President Carter's national security adviser peered resolutely with gun in hand at Soviet controlled Afghanistan from the top of a Pakistani military outpost high above the strategic Khyber Pass.
...
Zbigneiw Brzezinski, high White House aide, hesitated for a second and then declined an offer to fire the Chinese-made light machine gun toward Afghanistan.
...
The tour started with an early morning helicopter visit to a remote refugee camp in the Kurram Agency ... 12 miles from the Afghan border.
...
Brzezinski was careful not to promise military assistance to the rebels, but he told them of America's support for the efforts and said, "The entire world is outraged," by the Soviet invasion of Afghanistan.
The reporter was Stuart Auerbach.
Conclusion (re image 2)
This photograph of Brzezinsky and an unidentified Pakistani army major does not represent the forging of a strong alliance between Brzezinski and bin-Laden or between the USA and Saudi-Arabian led groups opposing the Soviet invasion.
Third Image: Gadaffi and Obama.
Handshakes
Here's the photo in the Washington Times on July 9, 2009

The article says
Libyan leader Moammar Gaddafi, who former president Ronald Reagan once denounced as a "mad dog," supped on pasta just two seats away from President Obama at the Group of Eight summit today and even secured a handshake with the U.S. president.
Gaddafi is attending the summit in his role as president of the African Union
So the president of the USA shook hands with the president of the African Union. There is nothing in the report to indicate that this particular handshake committed the USA to a strong and enduring alliance with the African Union.
The article continues
Denis McDonough, a White House official, said before the meal that Obama would not hesitate to greet Gaddafi. ''He doesn't intend to choose which leaders he'll shake hands with and which he won't: he'll be very happy to greet everyone he meets," he said, adding: ''He wants to see cooperation with Libya continue in sectors such as Tripoli's decision a few years ago to give up its nuclear program, an absolutely voluntary decision that we consider positive."
It can be plausibly argued that the president of the USA viewed his shaking hands with the then ruler of Libya as helping to encourage or reward a process of nuclear disarmament and a cessation of sponsorship of terrorism.
Alliances
If we look for an alliance using the dictionary meaning of "a formal agreement or treaty between two or more nations to cooperate for specific purposes."
One list of arms-control related agreements and treaties at http://www.armscontrol.org/factsheets/LibyaChronology includes
January 3, 2008: Libyan Foreign Minister Abdel Rahman Shalgam pays an official visit to the United States and signs a Science and Technology Cooperation Agreement. This is the first official visit by a Libyan Foreign Minister to the United States since 1972.
August 14, 2008: The United States and Libya sign the U.S -Libya Claims Settlement Agreement, providing full compensation for victims of the 1988 Lockerbie bombing and the bombing of the Berlin disco. Under the terms of the agreement, Secretary of State Condoleezza Rice certified to Congress that Libya paid $1.5 billion to cover terrorism related claims against Tripoli. The agreement also addressed Libyan claims arising from U.S. military actions in Tripoli and Benghazi in 1986 to the amount of $300 million.
Note Barack Obama was inaugurated as president on January 20, 2009.
November 20, 2009: Libya unexpectedly halts the shipment of the remaining 5.2 kilograms of HEU in spent fuel from its Tajoura research reactor. The material was scheduled to be flown to Russia for disposal that same month as part of an agreement between the Libya, Russia, and the United States.
there's no mention of any bilateral USA-Libya agreement or treaty signed on or around July 9 2009.
According to the state department, the following USA-Libya treaties are currently in force
Agreement relating to the termination of
outstanding agreements with Libya.
Exchange of notes at Tripoli February 5, 1972.
Entered into force February 5, 1972.
23 UST 82; TIAS 7275.
Agreement regarding grants under the Foreign
Assistance Act of 1961, as amended, or successor
legislation, and the furnishing of defense
articles, defense services and related training,
including pursuant to the United States
International Military Education and Training
(IMET) Program.
Exchange of notes at Tripoli May 2 and December 8, 2009.
Entered into force December 8, 2009.
NP
SCIENTIFIC COOPERATION
Agreement on science and technology
cooperation, with annexes.
Signed at Washington January 3, 2008.
Entered into force April 4, 2008.
TIAS 08-404.
ATOMIC ENERGY
Agreement to facilitate the provision of
assistance for the transfer of spent high-enriched
uranium nuclear fuel to the Russian Federation.
Signed at Tripoli October 28, 2009.
Entered into force October 28, 2009.
TIAS 09-1028.
CLAIMS
Claims settlement agreement, with annex.
Signed at Tripoli August 14, 2008.
Entered into force August 14, 2008.
TIAS 08-814.
DEFENSE
Military assistance agreement.*
Signed at Tripoli June 30, 1957.
Entered into force June 30, 1957.
8 UST 957; TIAS 3857; 284 UNTS 177.
Note
* Terminated February 5, 1972, except that Article I,
paragraphs 2 and 4, arrangements under Article I, para
graphs 3, 5, and 7, and under Article II remain in force.
Arrangement for return of equipment and
material no longer needed in the furtherance of
the mutual defense assistance program.
Signed at Tripoli June 30, 1957.
Entered into force June 30, 1957.
8 UST 963; TIAS 3858; 284 UNTS 188.
Agreement relating to the termination of
outstanding agreements with Libya.
Exchange of notes at Tripoli February 5, 1972.
Entered into force February 5, 1972.
23 UST 82; TIAS 7275.
Agreement regarding grants under the Foreign
Assistance Act of 1961, as amended, or succes
sor legislation, and the furnishing of defense
articles, defense services and related training,
including pursuant to the United States
International Military Education and Training
(IMET) Program.
Exchange of notes at Tripoli May 2 and December 8, 2009.
Entered into force December 8, 2009.
NP
SCIENTIFIC COOPERATION
Agreement on science and technology
cooperation, with annexes.
Signed at Washington January 3, 2008.
Entered into force April 4, 2008.
TIAS 08-404.
None of those was signed in July 2009 at, or near, the date of the handshake.
Conclusion (re image 3)
This photograph does not represent the forging of a strong alliance between Obama and Gaddafii or between USA and Libya.
Significance of Handshakes
Here's another handshake

There is no indication that this handshake commits the Democratic Party and the Republican party to a strong alliance.
Overall conclusion
The image in the question is a sloppy piece of propaganda that relies on fabrication, false identification and an exaggerated interpretation of the meaning of handshakes between politicians.