These are nut drivers, not phillips head drivers used for drywall screws. I suppose you could put your phillips head driver in a 1/4" one, but would not think that would work very well.
It sounds like you are looking for something like this magnetic drive guide: https://www.homedepot.com/p/Milwaukee-SHOCKWAVE-Impact-Duty-Magnetic-Alloy-Steel-Drive-Guide-Bit-Set-7-Piece-48-32-4518/303481468
Yes. 1/4 hex shank is very common
I'm very happy with all tools quality
5/16 and 1/4 inch what i bought