Can the core Profile module (it is deprecated) be used? And how will I upgrade? The profile core module is being deprecated in D7.  It exists and operates in D7, but is hidden and can only be enabled with drush or a custom module.  Drupal.org recommends that users now use Profile2, a custom module, but my attempts to do so have met with WSOD on several attempts. In fact, after enabling the module, it will crash the site if you try to disable it.  The problem links to a core issue, but even with the recommended patch, Profile2 still has other problems I have not been able to correct yet.

In the meantime, I enabled Profile, and it has desirable features I would like to implement.  My concern is that whatever I do may be lost in the future.  Since I cannot load Profile2, I do not know if it builds on Profile or I will have to reconstruct everything later.
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.