...are personal epistles (letters to individuals). For a defense of the authenticity of the Pastorals, check this article, which is where many of the links below go.
Doesn't Paul contradict Jesus in Matthew 6:5-6 here when he tells us to lift up their hands while praying? No, because Jesus' words are an instruction against public prayer, done for the purpose of being noticed ("that they may be seen of men"). 1 Timothy 2:8 has nothing to do with modes or positions of prayer.
What's the relevance of this, when Jesus says that what goes in a man does not defile him?
There is no relevance -- Jesus is explaining that it is not the external that makes a person unclean, but the internal (what one thinks, says, does) that makes a person unclean. Paul is not saying wine is bad, but that the abuse of it (internal problem) is not quality a bishop can have.