Hi
@Piggies&buns have given you our advice for when to clean with skin parasites. It is different to dealing with fungal ringworm spores, which are environmental. In the case of less harmful hay mites, these come usually with a batch of hay (hence their vernacular name), so getting rid of your current hay and sourcing it elsewhere is the best way of preventing further outbreaks.
As to hair cutting:
You need to cut short your hair only with hay mites, not mange mites because hay mites fix their tiny eggs to the hairs while mange mites burrow theirs into the increasingly inflamed skin.
When you feel underlayer hairs in the bum area in dark guinea pigs, the fixed hay mites eggs feel like minute beads on a very thin string; in light coloured piggies the eggs look a bit like somebody has turned a pepper mill over them.
The haircut is there to remove these hay mites eggs, so you then have to fight a lot less mites in the coming weeks. Without egg cases fixed to hairs, the next generation of hay mites won't have a chance to emerge and there is also a lot less space where any mites can fix new eggs.
Guinea pig hairs grow constantly, like human hair and will grow back to their genetically determined length in a matter of weeks. How long that takes depends on the breed. In short-haired piggies fallen out hairs take about a month or so to grow back.
Hair cutting won't work in the case of mange mites because the eggs sit in the skin. Any treatment will only affect emerging mites but not the mange mites eggs in the skin, which are usually kept under control by a healthy immne system. You get outbreaks of mange mites only if the immune system is still under contruction (babies), overloaded (pregnancy/nursing, which is when they are also transmitted to babies) or weakened through illness or old age.
Some rescue or breeder piggies can come with an mange mite egg reservoir in their skin but once you know that have one of those piggies you can usually keep any mange mites under control by treating promptly as soon as you notice the first signs of an outbreak; in that case, the well cared for mates usually can fend off mites with their own immune system and things won't get very far.
Lice are play crawly things you can see. In well kept domestic piggies, hay mites are now the most common skin parasite. No haircut required.