Changing All Notes in Score to New Key Signature

I am new to MuseScore and score writing software. I thought I knew how to change the key signature of a score. I downloaded a score from the MuseScore web site. It's in C. I need it in Eb. I can select the entire score and apply a new key signature. However, the notes remain in the same place. Presumably, if it was a C before, it should move to become an Eb. How do I do this?

Also, the score has chords running along the top of each bar. Are these entered manually? I thought they might be linked to the chords used in the measures themselves, but maybe not.

I apologize if this is something easy to do, but I've searched the manual and played with the software a bit, but I can't figure it out.

Thanks.