why the D7 never detected the shuttle

I think this one can be explained by the radiation - Scotty and Ortegas had to jury-rig something to track the D7, and they had the advantage of knowing it was there.

As for the stuff with Uhura and Kor…upon reflection, I think this might come up in the season finale, which seems to feature

Potential spoilers for episode 10

Some kind of time travel to proper TOS times.