Pavement vs Sidewalk
Originally a pavement simply meant a hard, paved surface which could be used for road traffic or walking. Indeed there was little difference at one point. It is therefore an ambiguous term. Sidewalk is quite logical in this respect (not all American usages are so supportable).
As for it being illegal for a cyclist to get off their bike and push it round a corner at a red light, then I'd like some case law? Does that hold true for getting off a bike and crossing over to the other side to avoid a no right turn sign? What the highway code says (and I know this is not a definition of law as such) is that a cyclist cannot cross the stop line at a red light. However, I'm not suggesting that - in the case I'm referring to you would be getting off the bike before the junction, not at the junction.
Of course, do it right at the junction and it's a bit more questionable, but I'd like to hear of cases. Indeed in some circumstances the Highway Code actually recommends getting off your bike and pushing it on safety grounds, albeit not under these precise circumstances. It would be a distinctly perverse law for prosecuting somebody for getting off their bike and pushing it round the corner in order to avoid being alongside a lorry or bus. Of course there are many cyclists that pay no head of red signals anyway or, for that matter, about the rules regarding not cycling on the pavement.
Incidentally, for those who want to try it, there is case law for motorists being found guilty of going through a red light by nipping through a garage forecourt at a junction by a traffic light. This is not advisable, not least because garages have CCTV...