The question about how to find out which bands are used was discussed here, but then nobody seemed to know the answer:
I suspect that it could be something that only the modem knows internally, that the ModemManager software never gets to know about that. At least as far as I know there is no way of checking which ban is used.
You can tell it to use only a subset of the supported bands, so I guess you can be certain that a specific band is used if you set that band as the only allowed (current) band. I mean, if you do the experiment of setting a single band as the only current band and then trying to use the mobile connection, then it will either not work (because that band is not possible to use at your location) or it will work and then you know it is using that specific band because it is the only one it is allowed to use.
Edit: of course what we really want is a modem that uses free firmware, then we could easily find out this kind of things. But I guess no such modem is available.