well, you aren't going to say which fan you've got, but the 100mm ones mostly vary in extraction rates from about 70 metres/hour to about 95 metres/hour. Builders usually fit the cheapest one. It might be clogged with dust or cobwebs, so might the outside grille.
I think you probably mean it comes on with the light switch, and you probably mean that the light (and therefore the fan) is used whenver the room is occupied. If not, it should be.
The time delay can usually be adjusted up to about 20 minutes, or you could get one with a humidstat that will run until it thinks the air is dry.
If the fan is actually extracting (try it with cigarette smoke) you can leave it running all day while you are out, for an experiment, and see if you come home to a dry bathroom. It will typically run for about 50 hours on 12p worth of electricity.
The more powerful fans will either need a bigger hole, or are intended to go out of sight (usually above a ceiling but can be boxed-in) and work through a duct
For example this one extracts up to 220metres/hour
http://www.screwfix.com/p/vent-axia-acm100t-in-line-extractor-fan/53730
To cure condensation, damp and mould, you have got to increase ventilation. Changing the paint will not remove damp.