Aluminium door on single brick wall

In theory you could fix the frame of the door to the brickwork..but..you need to consider the extra load placed on the single brick wall. You should have a pier tk brace the wall to give it rigidity and any extra load would be best put there. Single brick walls are laterally weak and gain strength when built as a "box"..so take care. Ideally consult a competant builder. If the wall has any perishing of bricks or mortar this is even more critical.

Yes if you are putting up an aluminium gate it will need a post then the gate will hook onto the post

it is better to attach the door to posts.

Ally is light but I would still say no, a single brick wall isn't very strong at all I would always put posts in with any gate just think if the wind catches it it wouldn't take too many times for the wall to fail.