In regular Buy Mode, you can find sprinklers under Sort by Function > Appliances > Miscellaneous Appliances (the 3 dots tab). If you Sort by Location, you go to Outdoor > Outdoor Activities. They will cover a 16-square area, I believe. As far as I've been able to tell, you cannot overwater plantings, so if you really want your gardeners to water by hand (just to give them more skilling), you won't hurt anything even if your sprinklers are on auto-water.
I suppose it's possible, because I always have difficulty finding them when I sort by function (
Edit: That's exactly where they're at, and is exactly why I have trouble finding them. How curiously inconsistent). And no, there is no way to over-water plants: your Sims will (or at least did) go and play in the sprinklers with every idle, waking moment of their lives...to the point to where you'd expect the lot would turn into swampland lol.
However, if you have auto-sprinklers you'll never get the chance to water the plants. You can't water them if they don't need it, and the auto sprinklers come on at 5am promptly...which is the time that the plants start updating. If you watch your garden, the sprinklers come on and one by one the plants that require watering will dry out and immediately turn green again. But if you have a decent sized garden, the experience to be gained by watering is relatively insignificant to the time saved. If you maintain one of each type of base game plant, you'll max gardening in a couple of weeks just from weeding and harvesting. This makes getting started with a brand new gardener difficult, so it would be a good idea to put at least some of the sprinklers into family inventory until weeding plants becomes an option.
While I'm about 50% sure on the handiness thing, you may be right about it being level 4. My handy sims are usually well past 5 by the time they get around to upgrading sprinklers lol.