Had hernia surgery with mesh. Would I be eligible for any bariatric weight loss surgery?

Yes,
You can still have gastric bypass after a mesh hernia repair.  It certainly will be smart to let your surgeon know about this history so they don't run into it by surprise.  The scar tissue left from the mesh may add a bit of time to your surgery but it should not markedly affect the operation or recovery.
Umbilical hernia repair is usually on the small side for the mesh patch; sometimes a larger hernia repair can require substantial changes in the usual surgical technique.

Yes, you would be eligible for bariatric surgery.    Sometimes there are quite a few adhesions, or scar tissue, that develops after the hernia surgery, but I have done quite a few of these and it is generally not too much of a problem.   Based on what you have described, I don't think it will present too much of a problem moving forward.

Yes, you can still have bariatric surgery. It may or may not make the bariatric operation a little more difficult, but there is no reason why you can't have it done.