you can hold a chord whichever way you want and feel most comfortable just as long the 3 notes that makes up a chord rings out clear. for example, i could bar my 1st finger over the 3rd to 1st string on the 2nd fret and my middle finger frets the 2nd string on the 3rd fret. it still makes a D. our hands differ from one individual to another, hence, how we hold chords and how we place our fingers over the fretboard differs. there's no right or wrong, it's just how comfortable and how practical is it.

yeah... if u like the song, you'd remember the chords. not necessary faster but you will put more effort into remembering the chord shape.

learn how to read tabs. dunno go google around how to read tabs. it's basically just fingering positions on what frets to press. do take note, though that sometimes the songs you want to play maybe of alternate tuning i.e. drop D. this means you will have to drop your fattest string, in a normal 6 string guitar means the 6th string down a step. if you're confused, google/youtube about drop D or DADGAD tunings. also, if you're playing acoustic, learn how to use a capo cause' some songs use capo i.e capo the 3rd fret and you will be able to play the song in standard G tuning without retuning the guitar.

the guitar is a very manual instrument. it's a transposable instrument unlike the piano where everything is laid out in front of you. wiki guitar to learn more of the instrument.