Yes.

You would not be allowed.

Airlines set their prices based on routes, not miles flown or anything like that.
LON-NYC is pried to compete with others in that market (e.g. undercutting BA, so that pax can get a better price if they are willing to suffer the inconvenience of backtracking) while FRA-NYC is another market altogether.

You can generally do this sort of thing at the close of your trip, skipping the last leg without penalty (though it is technically against the rules), but at the beginning, thet will just cancel you.

FWIW, there are some smaller airlines that might let you get away with it, but I certainly wouldn't try it with UA, LH or any other major international carrier.

And BTW - Welcome to FT!