So BBC2 shows totally separate programming from BBC1? I thought I'd heard that there was overlap. (In particular, I thought I remembered someone commenting on how Buffy the Vampire Slayer was shown at a reasonable time on one channel, but early in the morning on another.)
They mostly show separate programming. A very few, very popular BBC1 programmes will get repeated on BBC2 at a different time in the week, for people who missed the first showing.

Also, does highbrow mean more literary things, like, for example, the Pride and Prejudice series done a few years back?
Perhaps "minority" is a better description than "highbrow". A dramatisation of Pride and Prejudice is mainstream and would be on BBC1. A discussion programme about Jane Austen's influence on female emancipation would be on BBC2.

Are these the same sort of cable channels we have in the US, like MTV, the Comedy Channel, Nick-at-Nite, SciFi channel, etc., or are they British based channels?
They're mostly either US channels or European or British versions of US channels, but there are a few British cable channels too.

I'd been under the impression lately that the BBC had resorted to commercials. I guess that was a misconception based on scant evidence.
The BBC doesn't take paid commercials, but it does seem to run an awful lot of "self-commercials" these days -- not just trailers, but "isn't the BBC great" sort of messages.

Shorter? Most US commercials are 30s or 15s, at about a 2:1 ratio. How much shorter can you feasibly get?
The advertising breaks are shorter. A programme in a 30-minute slot will have 25 minutes of content on ITV, or 29 on the BBC. I think in the US it's typically more like 22 minutes.

Peter