If I want playing a song with fingerstyle(I mean is changing it from strumming to fingerstyle) this depends on different Tabs or I can change it every chord to fingerstyle? When I play a chord with Fingerstyle for example E chord I must start playing from 6th string or 5th string? And for other chords which one way is right? playing open string with the chord or not?
There are arpeggio patterns as wide as the earth is long. The study for guitar that really tries to educate your arpeggio is Mauro Giuliani 120 arpeggio exercises.
It really is tremendous not only for developing the right hand finger picking technique but also in the way that it teaches you rhytm and inspires you in the patterns it teaches.
Many an excellent guitarist has sharpened his teeth on this.
When finger-picking, it often sounds best to make the first note played the root note of the chord. On E, it'll be the bottom string. Each chord has its root on either the 5th or 6th string, except for D chords, which use the lowest D available in standard tuning on the 4th string open. (I'm not counting Eb!!). So, yes, fingerpick each bar using the appropriate chord/shape and use root as the first note.
You may well use 3rd or 5th of a chord as a variant to root, to produce a 'walking bass' line. Or if a chord is static, a 1-5 works well.