Does drinking magic potions allow you to hit harder or more often?

More often (barely), not harder except for slayer dart (possibly let you hit 1 more).

each magic spell has a cap damage that you are set ewith right away so like as soon as you get Fire bolt you can do 12 but never higher then 12 not even at 99

They let you hit more often and get hit less by magic attacks. Personally i feel magic potions protect from mmagic attacks more than a defence potion.

They're more useful for casting spells at a lower level, like enchantment or teleport spells.

It is useful to defense against magic attacks; for members with magic level who want to cast magic from 3 level higher, it gives access to magic temporarily, but i wont waste money on that if i were you...because of the time limit and cost