You're right in thinking 2L is a bit small. We recommend tanks that are at least 2.5 gallons (about 9L) for bettas. Bigger tanks don't bother most bettas, but if they do, they're BIG tanks (like 70 gallons). So upgrading your tank will make your betta very happy!
You can't fit a snail in a tank that small. I'd say you'd need 3 gallons and up for a snail.
By yucky stuff, do you mean algae, or fish waste? You can control algae by not placing your tank in direct sunlight, or reducing the amount of light that the tank recieves. Fish waste you will have to clean on your own, though. For a tank of your size, I'd recommend cleaning it every other day. But when you get a bigger tank, you can clean it less!
If you have any other questions, feel free to ask!