1. Yerba mate does contain caffeine and it does not depend on how you prepare it. Descriptions such as “mateine” are an attempt to explain the unique way yerba mate acts on the body, which is different than caffeine when present in coffee — but it’s still caffeine.
I know a lot of people who prepare it the way you do, but I don’t know of anyone “rebrewing” it because it is much weaker the second time around; however, there is nothing wrong with doing it that way. It really isn’t any different than continuing to pour fresh water into a mate gourd to make it last for hours.
2. Repeated use of yerba mate will stain your teeth, but not as much as coffee or tea. Regular dental visits will keep the stains in check.
3. Yerba mate really does contain all of the nutrients you’ve read about. Whether those nutrients will translate into a health benefit for you depends on many factors including: how your body reacts to the nutrients, what other sources of nutrients you already have in your diet and what nutrients your body may be lacking.

Looking forward to your response,
Adrienne

A few thoughts come to mind. First, I hope you do not let it stand in the tepid water more than a minute or two before pouring in the hot water. Second, I hope the water, while not “boiling” hot, is at least 140 degrees. Third, with tea bags, you may not see the froth around the edge of the cup, but you certainly should see it in the air pockets of the tea bag.

If you are using a French press, it could be that the froth is actually under the plunger and enclosed in the sleeve with the yerba where you can’t see it. I always see plenty of froth around the edges of the liquid in my French press however.

Finally, the froth usually appears shortly after adding the hot water. Even a few “tiny bubbles” around the edges will be a good sign. I have had a few brands that did not produce very much froth — but most quality brands available in the U.S. have a lot. Look again.