-Update - Solved -
Ok guys, finally I got rid of this problem...

Got the battery and alternator tested at local Autozone, both are fine. Initial test for the battery I got a 'bad battery' message, because the guy performed the test from the terminals in the front. Then we tested directly on the battery and it passed the test.

Next, test for parasite current (to discard a short). There was none.

Finally, following the advice in this forum, I ordered a new ignition switch from autohouse.com. It took me about 30 min to replace and now all the gremlins are gone. I have my steering wheel functions back, horn, wipers, vanity mirror lights.

Thank you guys for the help.

Next project: replace rear window regulator...