CSUDH (and Cal State Univ regents) own the land. AEG rents the land from CSUDH. AEG owns the stadium complex. LAG (and any other teams there, like the USSF) pay AEG for the use of the facilities. Kind of the same situation as at Staples Center (though I think AEG own the land it's on) where the Kings (which AEG own) pay rent (along with the Lakers, Clippers, Sparks, Avengers and any other promoters) to AEG for the use of the facility. Did I confuse you?
Concerts certainly. Possibly Mexican Nats (AEG I believe owns the rights to promote them on this side of the border now) I wouldn't be surprised to see some other stuff done there as well.
Pete Sampras Tennis Academy, there'll be at least one pro women's tennis tourney there, San Diego Chargers summer camp, I believe U.S. Track and Field, U.S. cyclying (velodrome), and probably some CIF (high school) championships. There's a rumor Bayer Leverkussen will train there next year during their winter break.
I can't imagine it would be the stadium field.. No way.. NFL pre-season is right in the middle of MLS's season.. There are lots of training fields also so I'm sure it will be one of those. An NFL team training would destroy the field.