Regarding your questions:
1) Yes night fighters are your friends since supply drops happen only at night. I normally use some of the LW airfields leaving them behind in troublesome areas. You won't see many kills though from my experience.
2) Garrison all the urban hexes to the maximum. Down south rely on the allies to hold the big cities (like Lvov or Kev or Stalino) since their security divisions contain numerous soldiers. Don't mix them together (Romanians and Hungarians) give them stretches of areas to guard (I normally have the Romanians guarding the area near the Black Sea like Odessa, Nikoliev and onwards to Rostov, while the Hungarians take the inland route of Kiev, Poltava and on to the Volga). In the north you will have to rely on your 2 rear commands who normally dispose enough manpower to handle the job - though keep an eye on Leningrad because if you don't garrison it well, you'll have a lot of partisan bands created. And yes, you'll need increasing numbers of formations to guard your back. Having said that, the only front line formations you'll ever need is a few mobile brigades for anti partisan sweeps.
3) Not many. Most of the fighting in the rear areas was within the remit of security commands. Keep in mind that there are a host of rather unsavoury formations (SS, Cossacks, local militias and whatnot) that don't feature in the game that participated in this guerila war. Also for most of the period in question, even the Brandenburgers were used in such sweeps. That changed only in the immediate area behind the front lines where armies conducted sweeps with various kamfgruppes and sometimes entire divisions, but normally partisans rarely operated in these areas.