OK So I just restarted a case that I messed up on and found out that I have to do the WHOLE thing over instead of just that section. Anyway, The game goes back to the beginning of the case (it's the first one with Bekowski) and then I get a call to go to a street crime that I already did. I looked in my stats book though and all the street crimes I did were saved - 7/40. And I'm pretty sure that this was the first street crime that becomes available, the Masked Gunman.

any street crimes you've already done  don't need to be done again. You can actually go into the "Streets of LA" mode and any you've done will be gray when not selected, and new ones will be red.

as for the separation, it is by desk and certain street crimes only appear at certain times of the day. Also, once you go into a particular desk's Free Roam and get into a cop car it wil tell you if you have completed all of the street crimes for that desk.

Street missions autosave immediately after you complete them. Another suggestion, if you want to restart something after you mess up, you can just press start and hit "quit" bringing you back to the main menu. Jump back in the game and you'll be where the game last saved, which is more or less close to when you quit. Should save you a lot of time.

If you choose to restart, the game actually tells you that all your progress aside from the case objectives up to that point will be saved.