Can I say
Today I am fasting/ I will fast/ I will be fasting/ I am going to fast
Tomorrow I am fasting/ I will fast/ I will be fasting/ I am going to fast
Today I am fasting.
Tomorrow I will be fasting.
NOT A TEACHER
(1) I think they are all correct, depending on the context (situation).
Tom: Would you like a big slice of chocolate cake with three scoops of delicious ice cream?
Mona: No thanks. I am fasting today./ I am going to fast today.
***
Alice: Would you like to join me for a delicious dinner later today?
Joe: I will be fasting later today, but thanks anyway.
***
Ramon: Excuse me for saying this, but I think that you have been eating a little too much food lately.
The Parser: Your're right! I have just made a decision: I will fast today. No food at all.
Ramon: Good idea!
(2) George: I want to invite you to my big pizza party tomorrow.
Patricia: What's wrong with you? You know that I am fasting tomorrow. I told you about that yesterday./ No, thanks, George. I will be fasting tomorrow/ I am going to fast tomorrow. But thanks loads, anyway.
***
Wife: What are you doing eating all that food? You promised me that you were going to go on a strict diet. Look at that big stomach of yours!
Husband: Ok! Ok! Stop nagging me! I will fast tomorrow. But today I want a delicious dinner.
Wife: Go cook it yourself!
Just to clarify I was giving the natural expressions that I have used and heard used. I was thinking of religious fast days. In that case, one is fasting for an entire day, so saying "I will fast today" does not happen. You either are or are not fasting on a given day.