The only way a screw could sheer in this situation would be if it were subjected to a "dynamic" load. i.e. a moving load such as repeatedly jumping up and down on it.
You have a "static" load. No movement. By all means use no12 screws if you're concerned.
The fixing is by far the more important consideration. You really don't need Rawlbolts or any kind of anchor bolt. Anchors are really for much heavier applications, such as fixing timber to a wall to carry floor joists. Joists are subject to traffic since you walk around on them. Walking traffic can cause the joists to bounce and creep. So a heavier fixing is needed.
Re: the brickwork.
If it's an older house, avoid fixing into the horizontal mortar joints. It may well be lime or at least very old mortar.
The distance between horizontal joints (vertically) is 3" in old brickwork.
Locate a spot behind where the mirror is going (so that the mirror hides it) and poke about until you can identify a horizontal mortar bed.
By measurement, draw a pencil line 1 1/2" up from the bed. You're now halfway up a brick. Drill on this line.
Vertical joints are 9" apart (horizontally). Similarly, avoid these when drilling.
When you have two holes marked that are smack in the middle of a brick each, then drill.
You've got your plugs. I would suggest screws of around 70-75mm length. (Make sure you drill deep enough to take the length of screw.)
Plugs for a no12 screw can carry a load up to 50kg (each).
Get your fixings right, and it'll be solid forever.