So it is possible to say, "it looks as though it's going to rain"?I would say that "like" is also more common in AuE. It would often be shortened informally to:
[It] looks like it's gonna rain.
[It] looks like rain [coming].
I would use your first form with "as if it's" or "as though it's" in a more formal setting.
Yes, this was certainly true 30-40 years ago and I remember teaching that "like" is only a preposition. To say "he looked like he'd seen a ghost" was quite non-standard in BrE and to me sounded particularly AmE. But times have changed and I notice that "like" is used this way by a lot of BrE speakers nowadays.I think that there is a reluctance to use "like" as a conjunction in formal BrE, though as a preposition it's fine.