I can only answer on some of these based on my recent experience at CGK. The immigration was a lot faster. If I remember correctly, from the time we disembarked the plane, immigration, picked up our luggage, went through custom and met the people who picked us up was 30 minutes. We also had two kids with us. So if there are only 2 of you, I am sure it will even be faster. Granted, we arrived at midnight so it was lighter. But then again, there were other planes arriving around that time as well. The immigration was very smooth and a lot faster than the previous ones I'd been.

You don't need a visa for UK nationals.

There are inter-terminal mini buses. I haven't had a chance to be on them. Thus, I can't really comment on that. Depending on timing - Cabs line can be long.

I think you'll be fine with the flight time you have. Enjoy your trip. I certainly can't wait for our next vacation back there.