Can the core Profile module (it is deprecated) be used? And how will I upgrade?
First of all, it's important to understand something MotoTribe has already mentioned. The most important functionality of "Profile" is now in for Drupal 7 new "users are entities" concept. Since this allows you extend users with fields, the profile module was considered redundant.

If I recall correctly, the main reason for it remaining in Core, was as a transition path from D6 Profile. In D8 I don't believe Profile will exist at all, and since it's already deprecated, I very much doubt there will be an upgrade path from D7 profile.

If we instead follow the trail of issues that follow from yours on the Profile2 queue, we find a Core issue, which is so far advanced that it has been applied to D8, and applies cleanly against D7 with full test coverage. I would apply that D7 patch, and try with Profile2 again.