The ? is very common in desktop software namely in Windows and macOS. Nevertheless both symbols exist in Material Design. Typically the i is a shortcut for quick information, and ? more extensive documentation as it is common in desktop software (the tooltip is an hover effect so when a user goes to the trouble of pushing a button it probably wants more than that).
For a touchscreen app, however, since Material Design accepts both symbols I would go with i. My arguments are:
1) It seems far more appropriate for what you are trying to do (small comment).
2) Your app already presents the ? mark at the top, so the i would create an healty contrast.
One last comment that, from my point of view, is relevant (although many times neglected) is that these kind of symbols typically appear in shapes that differentiate them considerably from other iconography. Note that the i and ? specifically appear as a circle in the great majority of software I have ever seen.
This might create some aesthetic problem considering other buttons in your app are also round but I would advise you to make some sketch tests to see what works best (intuitively your square info button doesn't seem right, but I can't seem to pinpoint exactly what is bothering me: the shape, the color, the choice of i, etc.; I would definitely draw some different models and see what comes up).
To answer directly to your questions:
1) I think the system you choose for the tooltip seems very adequate if the message is never big (so the displacement of the widgets never makes the user loose orientation).
2) I don't think your choice of tooltip is inconsistent with material design but you are right. I also can't seem to find any documentation regarding this specific point. hgshh hdsh hdsfh