302 redirects are temporary. Meaning that you (or whoever created that redirect) intend to remove it later, which means that yes, you should continue using the original URL if you still care about it.
Otherwise, just replace the 302 with a 301 (but be careful, if your original URL ranks in google and you 301 it then you're going to lose the rankings of the original URL. If you wish to keep the rankings keep the 302 redirect)
of course! Like I said, 302 redirects are temporary redirects, and google knows this so they'll keep your original URL in the SERPs for as long as possible