Is it ok to include garlic when I can hot peppers

The right way to know if your recipe is safe is to use a recipe from a trusted source. What you're doing is pickling, so just search for pickled pepper recipes. For example, I quickly found this one:

http://nchfp.uga.edu/how/can_06/pickled_hot_peppers.html

The NCHFP is one of the big authorities on canning in the US, so you can certainly trust that. You can add spices, and if desired add more salt or vinegar, but you don't want to use less - it might become unsafe.

And follow their process - there are reasons for everything. For example, all the boiling and details about how to fill the jars help guarantee that you get a good seal, so your jars will stay safe long-term. What you're doing is really prone to bad safety issues. For example, things could get colonized by bacteria while you let them cool, then you'd seal it in the jar and let it go to town. Or your seals could fail. You may get lucky for a long time, but not everyone will every time.

You should be able to find plenty of similar things from other universities, if you need, or you can buy an authoritative cookbook/reference.

Yes you can reprocess them in a water bath within 24 hours, and it should not ruin the jam. According to National Center for Home Food Preservation .

Reprocessing Unsealed Jars: If a lid fails to seal on a jar, remove the lid and check the jar-sealing surface for tiny nicks. If necessary, change the jar, add a new, properly prepared lid, and reprocess within 24 hours using the same processing time. Headspace in unsealed jars may be adjusted to 1½ inches and jars could be frozen instead of reprocessed. Foods in single unsealed jars could be stored in the refrigerator and consumed within several days.

If you want to reprocess all the jars, even if they seemed to seal, make sure you remove the lids and continue from that point. Instructions for water bath canning can be found here.