If I have 70% chance to avoid being frozen, and am then frozen, if I use a Taste of Hate to push my freeze avoid chance to 100%, will it remove the freeze since i'm now in the "immune" threshold?
There is no "immune" threshold. No amount of chance to avoid being Frozen can ever become equivalent to Freeze Immunity - because avoiding being frozen is inherently something which can only happen at the time you would be frozen.
100% chance to avoid being frozen is equivalent to "cannot be frozen" - both mean that no freeze can be applied to you. This does not do anything to freezes that were already applied.