@m4ng4 (I hope I'm tagging people correctly)
The lady with red hair is a person who works at the training center. He calls her because he doesn't know what to do with the monster corpse (since it's way too big for him to carry). I believe the dojo will be something that will be explained later...
@Wreavant The translations do seem to be off here and there, but the 1st part of it is essentially just him talking to himself, and the second part is when he's actually on the phone with another person.