This answer focuses specifically on Queensland's capital Brisbane, since its history is best documented, but the general principles would have applied to other towns as well.
1) Is it true that these streets were used to curfew indigenous Australians?
Yes, it is -- but the naming predates the policy. More specifically, boundaries were defined to set the city limits of many places including Brisbane. Per this page, which contains a wealth of historical quotations on the topic, Brisbane's boundaries including Boundary St were first defined in 1846:
... the government decided to bring Brisbane within the provisions of
the Police Towns Act of 1839. The town limits were drawn roughly into
the shape of a square, straddling the river. (45) Today the limits
fall with Boundary Street on the north and west, Vulture Street on the
south, and Wellington Road on the east. This act was aimed at the
removal and prevention of nuisances and obstacles, and 'for the better
alignment of the streets'. Wickham had complained in April 1846 that
dogs, apparently without owners, were 'constantly prowling about';
pigs and goats were also a nuisance rambling about 'in search of food,
destroying gardens, crops'. So the Police Towns Act and the Dog Act
came to apply to Brisbane.' (46)
(46) Police Magistrate to Colonial Secretary, 25 April 1846, (2 letters), 4/2735.2,SANSW.
Around 10 years later, a curfew on entering within the boundaries was imposed on Aboriginals:
From 1840 to 1855 Aborigines moved quite freely around the
settlements, but after 1855 Blacks were prohibited from venturing
inside Vulture and Boundary Streets after 4 p.m. or on Sundays.
Memoirs of the Hon. Sir Robert Philp, K.C.M.G., 1851 - 1922' by Harry C. Perry, Brisbane: Watson, Ferguson & Co., 1923
And in 1897, the Aboriginal and Islanders Protection and Restriction of the Sale of Opium Act (transcript as PDF) not only banned them from entering towns and cities in Queensland (unless lawfully employed or otherwise exempted), but allowed the government to forcibly move them to designated reserves at will:
It shall be lawful for the Minister to cause every aboriginal within
any District, not being an aboriginal excepted from the provisions of
this section, to be removed to, and kept within the limits of, any
reserve situated within such District, in such manner, and subject to
such conditions, as may be prescribed.
The Act remained in force (with some modifications) until replaced by the Aborigines’ and Torres Strait Islanders’ Affairs Act 1965.
2) Did it also apply to black US military personnel in World War 2?
No, this does not appear to have been the case. Now I can't prove a negative, but we do know that the US army maintained racial segregation at the time and the designated recreational club for African-Americans was the Doctor Carver Service Club at 100 Grey Street, South Brisbane. This was centrally located and well within the town boundaries, as Boundary St is some 5 blocks to the west and Vulture St well to the south. Among many other facilities the club contained a "swinging" dance floor and a dormitory, which would not have been compatible with a curfew, much less a total ban.