How exactly do Minh Thi Phan's unique abilities work? 

Does she gain one additional die on every skill check while having an ally / another investigator in the same location? Or does she simply add +1 to the result of every die rolled in  those skill checks?  I.e.: Do her unique abilities work like the one of the common skills ("Fight": +1 to fight checks) or like the grapple skill ("add +1 to each die you roll")?

I would say that it is +1 die (like the fight skill). Otherwise it would probably have said something like add 1 to all results.
The use of the word bonus is a bit confusing but not exactly the first inconsistent wording we've seen.

Yep, Tbla's right. Practically, it's like she has a permanent Voice of Ra granted by her ability. Needless to say, if you manage to have her passing her PS, it's kind of an unstoppable character :-)

@Julia:

This has been the way I've played it, too - until I read somewhere in the forums that some players play it differently (without mentioning why). I still prefer  "my" interpretation, but it (almost) never hurts to ask… ;-)