Yes, that's the root of the problem. I can't prevent the end-user from mounting network drives -- in fact, in the expected installation environment, the average user will have several very large network drives mounted.
I believe you.
Under Windows, installation takes about five minutes, and the full-disk search provides a nicer user experience if they're upgrading from an ancient copy of the software. Under Wine, I need to either skip the full-disk search, or warn the user that it may take several hours.
Again, I believe you. You've already gotten a couple suggestions on how to detect Wine, which you may use. We just don't recommend that, as the methods may not be supported in the future. Whether you choose to heed my recommendation is up to you ;-)
Still, it'd help if you could log a bug about it. Include which software it is, whether and where a copy is available, how network drives are mapped, and so on. Without a good bug report, we're rather less likely to fix it.
Out of curiosity, is the previous installation likely to be found under Z: ("/") rather than under C:? --Juan