First question - is it safe to give out the wallet addresses like I see in signature lines here and used for the purposes of drawings and donations?
Does this put the security of said wallet/bitcoin address in jeopardy?
Reusing addresses puts the privacy of you (lots) and everyone else (a bit, because everyone you send to/receive from is now linked to you whether they like it or not) in jeopardy. Don't put one in your sig. Make a fresh one every time.