yes open the window a crack to help steam/condensation out. consider an extractor fan if viable. (12 volt with transformer type not mains power direct.)
with regards the loo, if it's not a 'poor aim' problem it may be the cistern filling with cold water causes condensation to form on said cistern and that's what is dripping down.
flushing less often (water saving ) may help a bit.
i am assuming it's not down to a leak at the joint of the loo and cistern or the loo exit/waste pipe.check by drying it thoughly, then flushing and use a tissue to see if any wetness has suddenly appeared.