Isn't művésznő feminine form (nő) of művész?
Why "művésznő" and not "művész"?
müvész' = male artist; múvésznö = female artist
Why not 'ide' over 'itt'?
Because ‘ide’ really means ‘to here’ (or ‘hither’ in archaic English), even though it's usually abbreviated to simply ‘here’ in modern English. So ‘itt’ says where someone is, while ‘ide’ says where someone is going to.
why we can not say "a müvesz var itt van"? I read that when using itt and ott we should say van
The problem is that there is already a verb "vár" means waiting.
Note it doesn't mean a castle in this example.
So you either say "A művésznő itt van" - The artist is here or "A művésznő itt vár" - The artist is waiting here.
A művész itt vár.