I clean my boys at least two or three times a year. Charlie I clean a lot more often, just because he hangs out more and its easy just to splash some water one and get him nice and clean. I wouldn't suggest using any products. Just plain warm water, with some sterile lube if you need it. Cleaning too often with soap can actually cause an infection (even on a perfectly healthy horse) and can dry them out badly. Water won't do either of those things. I also consider it a normal and 100% nessesary part of male horse ownership. There is nothing more disgusting and painful than an uncleaned horse. Some of the owners of stallions that come in to be bred should be ashamed of their horse's personal (stallional?) condition.
I would never pay a vet $50 to clean my horse's sheathes
I can do it better myself. I can take more time, more care, and more calm than a vet would be. Some horses (GELDINGS ONLY!!!!!!!!!!!) need some sedation to help them drop down, and acepromazine can be very helpful for that. NEVER, EVER give a stallion acepromazine, EVER. I do my own sedation, so if I need a little something its not a big deal for me to take care of that, but in some situations a vet would be needed for that. One of the best times to clean them is after getting their teeth done
If you are like me and have the vet out to do dentristry, they are sedated then and once the vet leaves you can pounce and get them all shiny.
As far as age, I don't know... I've never bought a young horse
I wouldn't do much right off. But before they are bred I would definately be handling them there and washing routinely. There is nothing more fustrating and dangerous than having a stallion in to be collected and having him fly off backwards or kick if you touch his penis. I would probably start "feeling him up" around 6 months to get him used to it, maybe even every week so that its entirely normal for him. Then when he's a yearling or even a little bit older start actively trying to wash him, again with plain water, no soap. That's my two cents