Regarding the first one, I think it's an error, so I'd report it.
For the other two, Arabic uses three case suffixes, -u, -a, -i, which can also be in indefinite form, -un, -an, -in. So far in the course, it seems like different case endings are appearing randomly :/
2amirikiyy-un is actually correct here, and endings are optional on the last word before a pause in speech, so that's why 3arabii isn't 3arabiyyun, which it would normally be.
To make things more complicated, most names are indefinite, so come with an automatic -un ending, but a few are known as "diptote", and don't use the -n, just -u. I'm not sure, but Taamir might be one of those names, hence why it's Taamiru here. Or it could be an error.