With increased use (teenage lad start seeing girls) our bathroom is
clearly not properly ventilated - black mould seems to build up
everywhere.

Current ventilation is a fan, which came with a shower light. It's only a
small thing, so not up to the job.

I am reluctant to start punching more holes in the ceiling, and mounting
a fan to the outside wall is not possible. Could I get away with
replacing the current fan with a more powerful one ? Assuming the new fan
is bigger, would using step up/down adapters be viable ?

Once the ventilation is sorted, what's the best way to deal with the
mould that has gotten into the grouting ?