Yes you just hammer them in. Screw head is only for unscrewing if necessary.
Re depth into wall - if it were 40mm into brick I'd be reasonably happy, but I suspect your wall is 25mm of old plaster and then 15mm of brick, or actually mortar if you hit the wrong spot...
Personally I'd be happy with that head shape to fix plasterboard, after all plasterboard screws have a countersunk ("bugle") head. Some care is required not to over-tighten (over-hammer!) and damage the surface of the board. If you go for a head that's flatter then the screw head will sit above the surface of the board. Are you planning on skimming? How much head thickness will that hide?
You can get special fixings with a huge flat washer head, possibly plastic. (Do a google image search for "mechanical fixings for insulated plasterboard"). I think they're mainly used for (a) holding just insulation boards without PB, (b) when there's no adhesive and you're using many fixings and the heat conduction through the fixing is a concern. I think they need to be skimmed over. I suspect that the plastic ones will not survive a fire, and remember that's the only purpose of these fixings.
Re depth into wall - if it were 40mm into brick I'd be reasonably happy, but I suspect your wall is 25mm of old plaster and then 15mm of brick, or actually mortar if you hit the wrong spot...
Personally I'd be happy with that head shape to fix plasterboard, after all plasterboard screws have a countersunk ("bugle") head. Some care is required not to over-tighten (over-hammer!) and damage the surface of the board. If you go for a head that's flatter then the screw head will sit above the surface of the board. Are you planning on skimming? How much head thickness will that hide?
You can get special fixings with a huge flat washer head, possibly plastic. (Do a google image search for "mechanical fixings for insulated plasterboard"). I think they're mainly used for (a) holding just insulation boards without PB, (b) when there's no adhesive and you're using many fixings and the heat conduction through the fixing is a concern. I think they need to be skimmed over. I suspect that the plastic ones will not survive a fire, and remember that's the only purpose of these fixings.