The T-800 was able to go through time because it was surrounded by living tissue. The T-1000 could imitate living tissue, but it is made up of alloy metals, so it is not technically a biological organism, but neither was the T-800 or T-101.
Some possibilities:
- Maybe Skynet used a time machine with improved capabilities (apparently with
the letter-boxed laserdisc for T1, you can see a type of bubble enclosed
around Reese before he drops, so this may imply that the same type of time
machine was used in T2).
- Mimicking living tissue is sufficient. The mimetic polyalloy is capable of generating a 'living field' of some sort.
- The time machine in T2 is in a separate existence from T1 (refer to section 8 on time travel).
- The T-1000 was sent through wrapped-up in flesh. This is the most likely (but most gory) explanation. In _The Terminator: Tempest_ comic, an advanced plasma weapon is sent through time in the belly of a man. The same method may be extrapolated for the T-1000.
Regarding the destruction of the time machine, Reese would have been gone before the machine was destroyed anyway. He wouldn't know for certain whether it was destroyed or not.