tahiyyatul musjid

Q: When entering my local masjid shortly before fard salat starts, some people avoid sitting down before the fard prayer. They say this is so that they will be able to include the intention of tahiyyatul masjid in their fard prayer (they say that according to their madhab which I think is Shafie, the opportunity of tahiyatul masjid disappears when you sit down). I know that the opportunity of tahiyatul masjid is not nullified for us Hanafis by sitting down, but is it still recommendable for us to stand together with the others (i.e. not sit) even if we are Hanafis, to be on the safe side and to avoid ikhtilaf? I mean just as our books of fiqh says that it is mustahabb for us to redo wudhu after having touched a person of the opposite gender in order to avoid ikhtilaf.

Q: When praying our fard salat in the musjid, I was told that we can have the intention of tahiyyatul musjid included in the fard salaah or the sunnahs prayed before the fard. Does this apply also to maghrib salat (i.e. can we combine the fard of maghrib with tahiyyatul masjid), or is it different since that is a three rakaat salah? If it doesn't apply for maghrib, are there any other salaahs for which it doesn't apply too?

Q: Which should be read first, Tahiyyatul Musjid or Tahiyyatul wudhu?