You might not approve of where the “center” is in the US, but Democrats absolutely represent the center left and republicans represent the center right of the actual American electorate.
Yes, but since the US is a more right-wing country than the rest of the developed world (healthcare, death penalty, taxes...), that would mean the Democrats are "centrist" and Republicans "right." Characterizing based on relativity to the developed world seems much more fitting, since we're discussing it between people mostly from other developed countries and in a thread about Britain.
When it comes to abortion, it's more of a wash. By one measure, US is now more decentralized, less federal gov., thus more right wing. 13 US states have complete elective abortion bans at all times, thus much more right wing. Most other US states have somewhat more lenient abortion laws, roughly ~6 weeks longer in general, thus more left wing.
If that's your best and only example, it only substantiates my case.