Question

medaaaaaaal :D
An open position chord

uses open strings

uses a barre

is movable

does not use open strings

Answer 1

I think A uses open strings but am not to sure

Answer 2

you're right

Answer 3

A chord can be played in many different voicings, some open, others closed. You can bar an A if you play it like this:
e---5
B---5
G---6
D---7
A---7
E---5