"given that" asserts that the first thing is true.
"Given that he stole once, he will steal again." - There is no question that he stole once; he did.
"provided that" suggests that thie first thing is hoped for.
"Provided that we can make it over the mountain by dark, we will be fine." - If we make it over the mountain, we will be fine. We do not know if we will make it over the mountain, but hope so.
"supposing that" - Actually, I don't use this form for an if - then statement. I will say something like "If it needs cooking, we will need a stove," or "Assuming that it needs cooking, we will need a stove."
"Supposing that it needs cooking, we will need a stove." - sounds okay in conversation, I guess.
"Supposed that it needs cooking, we will need a stove." - sounds wrong to my ears.
"If they supposed that the party is still on, they would be here by now." - sounds fine, but in this case, "supposed that" is not used as "if"