The HEX platforms at T2/3 are actually a little closer to T3 than T2 - you'd want to allow just a handful of minutes longer to get to T2.

Conversely, the Underground station is much closer (relatively) to T2 - perhaps half the distance.

I have to admit I've never counted the number of carriages on the trains - I just know the spot to stand at on the platform at Liverpool Street to end up by the stairs leading to the exit barriers at Paddington!

Just for information if you have to do this again, there is also a ramp onto the main concourse at Paddington just after you turn right after walking through the semi-open air passageway from the Underground station. It's a longer route than the steps which are 15 yards further on which go directly onto the platforms, but it does allow step free access without heading right round past the taxi rank.