Threadfins and Dwarf neons would be suitable, you could have around six in your tank.
Looks great!
Also about the snails, these often come in on live plants and can multiply very quickly. The most common ones are Apple snails.
Actually the snails you have are most likely Apple snails. I think you could increase the shoal of tetras to around 15 fish, but I think 18 would be pushing it.
Rainbowfish are very nice to look at and Rams make excellent additions to finish off the stocking, for the cardinals the larger the shoal the more natural it will look.
Corydoras won't eat algae unfortunately, how about a few shrimps?
They'll be fine with the other fish and they are quite easy to look after, they obtain most of their food in the form of algae and they will also eat remnants of fish food.