Could it be possible to have a partial break up of the Soviet Union, where they lose control of Central Asia, the Caucasus and the Baltic countries, but keep Belarus and Ukraine? How would this affect the development of the 1990s and beyond?
eh, btw, wasn't that the central asian states that stick most to the soviet union?
A Russia with Belarus and Ukraine especially appended would have 60 million more people and much more of its formerly state-run industry intact. Assuming someone like Putin still comes to power and reins in overt lawlessness a bit, Russia would throw significantly more weight internationally.
Stronger Russia is almost bound to act to "protect" russian-speaking population in Baltics and Central Asia. It theoretically could alleviate some problems with direct and indirect discrimination of such population but only if all sides are reasonable, which is frankly unlikely to happen. More likely stronger Russia will try to resolve situation with force, though maybe not outright annexation.
Would political union of the Baltic states after exit be at all possible?
Not willingly, if anyone hates the Russians it's the Balts.
What happens to the second-level autonomous republics in this case? IOTL they were "promoted" to first-level republics once the SSRs had left. Would Ukraine and Belarus be willing to share billing with Chechnya, Tatarstan, et al?