There are several ways of translating the sentences you're posting here. I'll do my best:
- Mas te vale que a mi no me quieras convencer
"Don't even try to convince me" or "You better try not to convince me". Those are probably the closest two, although the first is slightly a long shot I believe it has the same "true" meaning.
- (con esa carita) de galán de feria
"With your baby face of run-of-the-mill attractiveness" which, again, is not exactly the same word-by-word but idiomatically has the same meaning.
- (este corazón) ya viene y fue de vuelta
"(This heart) has been already there". Again, the idiomatic translation. The literal one "(This heart) already went and comes by now" is not exact, and although both can be used you'd always prefer the one that is closer to the original meaning (I know the song, it was quite a hit here in Mexico).
- le cambie la letra a tu canción
"I re-arranged the lyrics of your song". Literal AND idiomatic, won't find anything closer.
- (yo no necesito ningún) vigilante: vigilante - bodyguard or watchman?
"I need no bodyguard", watchmen is an old term and is almost always used when talking about someone who watches over a place, not a person.
Hope this helps.