There is never one mouse, mice do not come in ones unless dropped in the house by a cat.
Remove all food sources (or put it in mouse-proof containers) and stuff they can hide behind/nest in.
You may see mice during the day where theres a population explosion and they are forced to venture further/out into the open to find food and water.
Mice are not harmless, they spread diseases, lepto and hantavirus being two pretty unpleasant ones.
Humane traps may not kill the mouse, however if you dump them close to home they'll return. If you dump them a long way from home they'll die trying, or die because the area you dumped them in doesn't support mice, or has a high predator population... or you dump them in an area that does support mice and they're killed by the resident population (they are vicious little bastards). Humane traps are merely passing the buck so you don't have to take responsibility for killing something.
Snappy traps are the most effective kill traps - they don't suit all locations though, they need to be placed where mice will naturally go, where you can check, without disturbing them frequently (or you put the mice off from visiting the traps). Sometimes, poison is the only effective way to deal with a big infestation.
Pest controllers charge by size of the property as this affects how much work they have to do, product they use etc. They need to know this in advance or they may not bring enough traps/poison with them or allow sufficient time for the job.
Really not sure what the relevance is of the visiting fox. Having a visiting fox certainly doesn't mean you only have one mouse!