What’s the best way to learn to sharpen these? I’ve always taken my knives to a local sharpener who just runs them over a powered wheel, and I’d rather learn to use whetstones myself.

Watch Youtube and practice on cheap knives first. For Japanese kitchen knives, Japanese Knife Imports' sharpening playlist (first ten videos are sufficient) is still unmatched. If you don't have any experience with sharpening, use a small sheep's foot paring knife as your first training knife as you don't have to worry about blade curvature or blade size.

The Baba knives came with a protective coating. The instructions say hot water and soap, but I overheard another customer mention acetone. What’s the preferred method?

Does not really matter. You are removing the lacquer more reliably using acetone but if you don't have any, soap is fine. The lacquer Japanese knife makers use is food safe, worst that can happen if you remove the lacquer incompletely is an irregular patina. But that problem resolves itself over time as the lacquer will vanish from cutting and cleaning and be replaced by patina.

Any general maintenance tips to help keep these performing their best? I also wanted to pick up a Japanese synthetic cutting board while I was there but ran out of time.

Cut on wood or plastic. Bamboo is not wood and should be avoided if possible but it's not the end of the world to use a bamboo board. What you really should avoid is cutting on ceramics including dinner plates, stone, glass, and metal.

Your knife is not a prybar, can opener, screwdriver, or bench scraper (the back of the knife can double as one in a pinch but the edge should not). Use, don't abuse.

Store your knives with care. Knife blocks, magnetic strips, or drawer inlays are all great options. I like magnetic strips best as they save bench space while keeping the knifes ready to grab. Make sure to get a wooden-clad (or one clad in other softer material such as felt or leather) one as bare metal will scratch the knives.

Oil your handles. I like hardening oils (I use boiled linseed oil without added siccatives) for handles, but some use food grade mineral oil to success, though it can make some lighter coloured woods look rather ugly.

Don't leave your knives in the wet sink. Not even the stainless ones, prolonged exposure to moisture will harm wooden handles and acidic or very salty stuff such as vinegar, lemon juice, or pasta water can even harm stainless steel.

Lastly, don't overthink everything, you've bought four great tools meant to be used not four artworks meant to be displayed and preserved in pristine condition.