For the first issue:
Looks like the dnd 5e system in FoundryVTT has been updated recently, with some breaking changes to its actor format. I can confirm character imports don't work with MBPMB to FoundryVTT 1.1.1 and dnd5e 2.1.5. I'll look into this, this might take some time depending on the severity of the changes.
As a workaround, use dnd5e 2.0.3 for now.
As for the second issue:
It seems one of the class features isn't formatted as expected:
- Martial Arts (Monk 1, SRD 26) [1d4]
- Unarmored Defense (Monk 1, SRD 26)
- If I wear armor/shield, I lose Unarmored Defense, Martial Arts, and Unarmored Movement
The application expects the format FEATURE (CLASS CLASS_LEVEL, SOURCE SOURCE_PAGE) while the third class feature seems to be a custom one. I'll adjust the class feature logic so it's less strict about the format and can fall back on a simpler way of adding class features if needed. Expect a fix for this in v1.1.2.