#1
How to choose a subject that is influenced by the music style you play ? Is there really a way
so that anyone can write lyrics ?
Also are songs* built on lyrics or lyrics built on songs

*By writting song I mean rhythm and melody of instruments
#2
Anyone can write lyrics. As far as the other questions, there are really just no right or wrong answers.
There's no such thing; there never was. Where I am going you cannot follow me now.
#3
Anybody can write lyrics, the quality will depend on practice and amount of reference of other lyrics

Now, the song -> lyrics / lyrics -> song debate is really easy: sometimes the song comes first and inspires the lyrics, other times the lyrics come first and the song is inspired by them. None of them is a good/bad option, however.

The subject is something you choose. You may choose a subject that is similar to those that your favourite bands use, but that's all to say about it.
Stand on your feet, partner. We've still got things to do.
#4
All sorts of genres can include all sorts of lyrics. Lyrics are a form of expressing emotion, and is a piece that morphs into whatever you're performing. Rhythm, melody, types of instruments, all don't matter when it comes to songwriting. If you're singing a line you've made years ago and you regret about singing, then you're not writing your lyrics right. Don't fight the emotions just let it flow all around you...