During the first month or so after my stroke, while my nervous system was busily rewiring itself, I experienced all sorts of transient proprioceptic illusions.

One of them amounted to the absence of the feeling of free will... I experienced my arm as doing things that seemed purposeful from the outside, but for which I was aware of no corresponding purpose.

For example, I ate breakfast one morning without experiencing control over my arm. It fed me, just like it always had, but I didn't feel like I was in control of it.

To give you an idea of how odd this was: at one point my arm put down the food item it was holding to my mouth, and I lay there somewhat puzzled... why wasn't my arm letting me finish it? Then it picked up a juice carton and brought it to my mouth, and I thought "Oh! It wants me to drink something... yeah, that makes sense."

It was a creepy experience, somewhat ameliorated by the fact that I could "take control" if I chose to... letting my arm feed me breakfast was a deliberate choice, I was curious about what would happen.

I think that's what it feels like to not experience myself as having free will, which is I think close enough to your second question.

As for your first question... I think it would feel very much like the way I feel right now.