You might get a clamp on type fixture and put one of the daylight type spiral flourescents in it or even a desk lamp sitting beside it. Make sure it says 65 or 6700 K on the bulb or package. 9 watts would be more than enough for this size.
If the tank does not grow algae, you will have to feed them something. Snails will eat anything, a bit of fish flake or pellet. Shrimp would need one pellet, maybe every two or 3 days, if they are the cherry type of shrimp, quite small. Careful not to give much food, as it will rot if not eaten. Mystery snails can get to be golf ball size and they lay eggs outside of the water. So they may crawl out if they are trying to spawn. You do need both sexes to get eggs though.
Nerite snails also crawl out, but not to spawn. It's just something they do. They can last for a long time out of water, they live on tidal flats where the tide goes out and leaves them exposed. So if you get a Nerite, and it sits on the edge, don't worry unless it falls out.
I would think you would change the water every few days, by scooping out about a quarter of it with a cup and replacing that with fresh water you have treated with dechlorinator first. Same temperature as the tank water is.
Plants will probably have to be trimmed back fairly regularly, as most would soon grow taller than the bowl. But it need not be hard work, just a pair of scissors and clip off the tops when they start to emerge from the water. You can reroot most cuttings now and then if older plants start to lose their looks, which saves buying new ones.
You may have to add a very small amount of fertilizer to the water to keep the plants looking really good. Choose plants that are low maintenance and lower light, they'll be less fussy. A small crypt species would look nice, and not outgrow the space for a long long time. But it would want a fertilizer tab in the substrate a few times a year, as they are heavy feeders. Stem plants grow taller, crypts grow more widely, from a central crown.
Shrimp, if you get shrimp, really enjoy picking at mosses. There are several moss species you could try. Java is common but not the most attractive. Christmas or Flame moss is much prettier and can be trimmed for size and shape.
There are liverworts too that are quite interesting and slow growers, known as pellia. There is a mini type, which is harder to find, the standard type and a very large leaf form called subwassertang that's becoming popular. Mosses and liverworts can be tied to rock or wood and will eventually take hold on them and stay on by themselves, then you can remove the tie. Thread or fish line works fine. A small twig or rock could eventually look like a shrub or small tree with these species.