Create a prediction formula from data input
I'm not sure if I understood your question! Probably better to plot a scheme at least. But according to what I guess from your question:

Q2- You probably need a simple MLP (Multilayer Perceptron)! it's a traditional architecture for Neural Networks where you have $n$ input neurons (here 20-25), one or more hidden layers with several neurons and 3 neurons as output layer. If you use a sigmoid activation function ranged from 0 to 1, the output for each class will be $P(Y=1|X=x)$.

Q1- So your question probably is: how many training data you need for learning a model? and to the best of my knowledge the answer is as many as possible!

and about the last question, I really could not figure out what you mean. You apparently have a very specific task so I suggest to share more insight for sake of clarification.

I hope I could help a little!