3 Neons: they really need more than 6 to be happy, they are a schooling fish that needs company of their own. Either get 3 more or take them out.
2 Guppies: Fine in a 10 gallon, just be careful for babies if they are male and female.
2 ADFs: Fine in a 10 gallon, just make sure that they are being fed enough food.
1 Cory: They need at least 6 to a group and if you have that in a 10 gallon, you would overstock it. Give them back to the LFS.
2 Otos: They prefer groups of at least 4 and unless if you are feeding them enough food, it would not work in a 10 gallon tank.
Shrimp: You can keep them in there, they clean up the extra food and have very little bioload.
Mystery snail: You can keep it in there.
So either get rid of the Neons and keep the Guppies, or get rid of the Guppies and get 3 more Neons. Fish you will need to take out for sure are the cory, and otos.