I haven't seen my "trainers" lose any influence points. It could be that your trainer has some negative trait that deducts influence per turn. The most important point about trainers is that they have to be active (fight battles every turn or so or govern and build a lot). The trainee will gain xp and influence at the same rate as the trainer (pretty much). In a sense, you get a double whammy.
If the trainer is inactive, both characters are likely to develop negative traits.
As to marrying a foreigner: you get a diplo boost with the faction of the bride. It shows up in the diplo relations screen.
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