The cloudiness may not be directly related to the cucumber. It may be a bacteria bloom -- quite common in a tank that's starting to cycle. Usually it goes away in a few days.
Tetra Safestart is a great way to speed up the nitrogen cycle. You still want to keep an eye on ammonia and nitrite readings, and change water accordingly.
If you haven't seen this yet: CYCLING: the two-sentence tutorial
Let me know how the cycle goes for you. I'm interested.
Your Betta might be avoiding the snail because it's a new thing in the tank. He'll get used to it. By the way, my Nerite as been living in a 5g with a Betta for years now. I've never fed it anything. It lives fine on what little algae it can glean from the plant and tank surfaces.