I guess it depends on how you define free will exactly. Of course you can't suddenly decide to violate the law of physics, but within those laws, you can more or less do what you want.
Of course there are other limitations, like the ones society and your life circumstances impose on you. Ultimately, it's always a question of the definition. But if you tweak the parameters so that we only consider choices that are actually possible, then yes there is free will
No. A very, very complicated set of physical states produced in you the "decision" to flip the coin. Laws of physics controlled in a nearly-impossible-to-predict but still totally deterministic way whether the coin turned heads or tails. This condition set off a number of other conditions in your brain, with neurons firing in precise patterns that result in your decision. This is, essentially, in no way different from simply thinking about the problem and coming to a decision on your own. All the step of flipping a coin does is use a different set of deterministic, physical principles to end up at your decision. Now, maybe the types of conclusions reached when you use your set of conditions called the brain produces results that make more sense to others than when you use the set of conditions called the coin flip, but in the end it's simply atoms and molecules interacting with other atoms and molecules in exact, deterministic, and insanely complicated way.
In the end, though, I feel this is moot. The human brain is not in any way set up to interpret or handle this kind of worldview. It's fascinating to ponder but useless in any actual implication. The core concepts of things like "society," "morality," and "justice" are technically incorrect but completely vital for people to be happy and fulfilled, because happiness and fulfillment are simply brain states.
I don't know, and I don't think it matters really. If I have freewill, I should act based on that fact. If I do not have freewill, my actions are determined by forces beyond my control, so it doesn't matter what I try to do.
Basically, by assuming I have freewill, I can't go wrong, because if I am wrong, there isn't a damn thing I could do about it anyway.