This article is from the The Terminator FAQ, by Karsten A. Loepelmann firstname.lastname@example.org with numerous contributions by others.
The Terminator 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
1) 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).
2) Mimicking living tissue is sufficient. The mimetic polyalloy is
capable of generating a "living field" of some sort.
3) The time machine in T2 is in a separate existence from T1 (refer to
section 6 on time travel).
4) 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.