1) What STI tests should I ask my new sex partner (male) to have?
There isn't a general list of tests that's recommended for males. He would probably be well served by chatting with a healthcare provider to see what tests they might recommend based on his risk factors. It's not a bad idea for anyone who's been sexually active to have an HIV test at some point; other common STDs for which testing might be sought include chlamydia, gonorrhea, and syphilis. Again, there isn't a one size fits all approach to testing.
2) If these tests all come back clear, is it safe in terms of STI to have unprotected (no barrier) sex?
No, not a 100% guarantee. A clinic isn't likely to test for everything as a "catch-all" approach. Some STDs, such as HPV, don't have a test that's approved for use with men. Other tests are based on finding antibodies (substances produced by our immune system in response to an infection) and may not be reactive, say, a few days or weeks after someone is exposed.
3) My culture from 3.5 weeks ago showed genital Hsv 1. We believe I contracted it from his oral hsv 1 because I have never had any oral or genital symptoms until this my first outbreak after genital contact with his saliva. If this is in fact the case (that I contracted it from his oral herpes), what is the risk for him now to contract genital hsv 1 from me?
There's no specific figure to say the risk is "____ %" It's obvious the virus can be transmitted while there's an outbreak, but there will be some time each year when the virus is active even with no symptoms present. Now, this probably happens far, far less with genital HSV-1 as compared to HSV-2, but the issue is you don't know for sure just when.
A reasonable risk reduction plan is not having sex while symptoms are present and perhaps using condoms at other times.
4) Is there a chance I had it prior to him, with no symptoms, and it just so happens that sex with him activated it? If so, does this increase his risk for contracting genital hsv 1 from me because what I have now might not actually be "his" herpes?
He could still get genital HSV-1 even if he already has oral HSV-1, but would be much less likely to have noticeable or frequent outbreaks.
5) What % risk does he face, for both scenarios?
See answer to #3 above.
6) I have faint red spots that linger 4 weeks after beginning the initial outbreak. But the skin seems to be intact, and overall I am so much better, not itching or swollen and no discharge or "weeping." It seems to just be like what's left after a scab has healed. What kind of sexual contact is appropriate at this stage?
It depends on whether or not the spots in question are related to herpes, and it's not clear if you're certain about that. If in fact it is a lingering symptom, then assume the virus can be transmitted. Herpes symptoms usually don't last much more than a few weeks, though, so if it doesn't seem to clear have it checked out to make sure it is in fact related to HSV.
I hope this helps.