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1: Do you believe that the mind plays any role in magick? Yes.

2: Are your will and intent the same thing? No. Intent is your motivation, the reason you want something to change or happen. Your will is what you want the outcome to be.
3: Can magick be performed just mentally (ie only in the mind) Yes magic can, through meditation, astral travel into other worlds, focus of the mind.
4: How much of magic is mental and how much is magick? At least half of it is mental. Magic is very dependent on knowing your own mind, how to focus it, how to use it to visualize your will and what triggers to use to generate the proper energy through your emotions and thoughts.

1: Do you believe that the mind plays any role in magic?

Depends. If you're doing it as a practitioner, than necessarily it is going to involve your mind in some fashion no matter what you're doing. If the magic isn't being done by or interpreted by a person, then one could call into question if "mind" is an appropriate word to use.

2: Are your will and intent the same thing?
rofl Intending to do something and actually having the will to carry it out are very often two different things. Intentions can be boundless, absurd, and unrealistic. Will is not boundless, as it is constrained by context. I can intend to grow angel wings all I want, but genetics are going to keep me from developing them in the "real" world no matter how much will I stuff into it.

3: Can magic be performed just mentally (ie only in the mind)
This presupposes that the mind is separate from the body, which I think is a questionable assumption. One doesn't need "props" to do magic, but I wouldn't say that means it is purely mental; the mind is part of the body. Try doing a spell with your mind when your body is dead tired and you'll probably see what I mean.

4: How much of magic is mental and how much is magic?
I'm not sure exactly what is meant by this question, but I interpret this as meaning "how much of magic is really just our minds tricking ourselves (aka, the psychological explanation for magic)?" Much of it. All of it if we're taking an empirical perspective; if it is empirically verifiable it becomes science, not magic; all else is "mere" placebo or training your brain. This "mere" placebo and brain-training though, really is nothing to sneeze at. Conventional medicine is finally starting to take it seriously as it can drastically influence how well we recover from all sorts of troubles.