For the first claim - that preparations were underway for a Ukrainian offensive in Donbas/Crimea - I perused the Wikipedia article on the Prelude to the 2022 Russian invasion of Ukraine and didn't see anything. The closest was this source, which does say that Ukraine had prepared some measures (including military ones) to reintegrate Crimea. However, this makes no mention of Donbas, and there's no indication in both this source and the Wikipedia article that Ukraine actually attempted to put those plans into action:
According to the press service of the head of state, the document defines a set of measures of a diplomatic, military, economic, informational, humanitarian and other nature aimed at restoring the territorial integrity, state sovereignty of Ukraine within internationally recognized borders through the de-occupation and reintegration of Crimea.
For the second claim - that Ukraine announced the possible acquisition of nuclear weapons: Ukrainian president Zelenskyy did apparently hint at this in early 2022:
Since 2014, Ukraine has tried three times to convene consultations with the guarantor states of the Budapest Memorandum. Three times without success. Today Ukraine will do it for the fourth time. I, as President, will do this for the first time. But both Ukraine and I are doing this for the last time. I am initiating consultations in the framework of the Budapest Memorandum. The Minister of Foreign Affairs was commissioned to convene them. If they do not happen again or their results do not guarantee security for our country, Ukraine will have every right to believe that the Budapest Memorandum is not working and all the package decisions of 1994 are in doubt.
The nuclear weapons aren't mentioned directly, but Zelenskyy did mention the Budapest Memorandum, in which Ukraine (and Belarus/Kazakhstan) gave up nuclear weapons for security guarantees. I imagine the idea is that if "all the package decisions of 1994 are in doubt" then Ukraine can reacquire nuclear weapons. That's certainly what Putin thought since he argued in the linked article that Ukraine is capable of acquiring nuclear weapons easier than most countries (i.e. Ukraine is nuclear latent).
The Ukrainian ambassador to Germany said something similar in 2021:
Ukraine will consider arming itself with nuclear weapons if it does not become a member of the NATO military alliance, the Ukrainian ambassador to Germany said.
"Either we are part of an alliance like NATO and contribute in this way to making Europe stronger ... or we are left with the other option, which is to arm ourselves," Ambassador Andriy Melnyk told Deutschlandfunk radio Thursday.
Kyiv would then "perhaps also consider its nuclear status," he said. "How else can we guarantee our defense?"
Edit: the BBC fact-checked the latter claim and concludes that although Andriy Melnyk did say it was possible, there's no evidence Kyiv was actually seeking to acquire nuclear weapons.
However, the Ukrainian government has not expressed an intention to acquire nuclear weapons and a military strategy document published last year did not refer to them ... The UN's nuclear watchdog, the International Atomic Energy Agency (IAEA), says it has seen no signs in Ukraine "of the diversion of nuclear material, intended for peaceful activities, for other purposes."