Your questions are the two most fundamental business-related questions of a website (well, anything we do in life, if you think about it, including living a life!). Thus, they are naturally the hardest ones to answer -- because such answers only reveal themselves with time.
There's simply no way to gauge interest. People have made money off the web in so many crazy ways (some kid makes $1K a day with a free breast implants site), you simply can't predict what's The Next Big Thing. In hindsight we think we see previously unrecognized signs of promise, but the truth is that nobody knows because there never was anything to know -- the present is fleeting, and thus decisions, which can only be based on the present (present feelings, present ideas, present outlook, etc.), will not have the solid basis they appear to.
Likewise, there's no way to forecast profitability (I mean, come on, free breast implants???). This is proven by the fact that you can analyze anything to death because there's just no way to ever have enough data to take a perfectly well-informed course of action. So the key is to minimize risk, right? But the more minimal the risk, the less likely the profit! Not that lots of risk means increased chances of a profit, necessarily, but less risk does correlate very strongly with less reward.
Now, having said all that, here's what I would would guess....
Yes people would be interested, especially if the benefits are expanded to somehow include useful diagnostics based on the statistics...though I'm envisioning some kind of "widget" to enable all that, of course, whereas you sound like you're relying on self-reported stats.
As for profitability, other than Adsense, which seems to only pay off with insane traffic (thousands [that's plural] a day if you want to see "real" money), your best bet would be some kind of referral service for your visitors...say, based on their IP addy, your site would make an educated guess as to their zip code, and pair that datum with any list of local music teachers, or instrument tuners -- shops, etc. Also, of course, Amazon Associates, for any books, etc., that happens to fit your service ("Appegios for Smart People DVD").
Your biggest immediate hurdle will be the programming involved...unless you plan to hire someone to do it -- which, of course, means at least a thousand, even if it's a friend majoring in Computer Science....
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