Will negative GMP and positive online GMP still hurt morale

Sleeping or stunned enemies will remain in toilets and dumpsters indefinitely.

The only way that they will woken is if you take them out, or if another enemy happens to check (specifically a toilet) as part of an alert clearing.

Offline materials come from three sources:

• Materials you pick up in the field. Processed materials in small crates go directly to your material totals every checkpoint. Unprocessed materials in containers go into an offline queue.

• Periodic conversion of materials in the offline queue. Every time this conversion ticks, 10% of your unprocessed materials are converted to processed materials.

• Periodic mining done on Mother Base itself.

Online materials come from two sources:

• Periodic conversion of unprocessed online materials. The conversion rate here is 30%. You get unprocessed online materials by extracting crates or as rewards in FOB missions.

• Periodic mining done on your FOBs. The amount of each material you gain at each of these ticks depends on the quantity of material deposits where your FOB is located (which you can see when you purchase the FOB or in the FOB information screen).

The offline sources can only tick while you are actively playing the game. The online sources tick in "real time," more or less, so you can stop playing for a while and come back to find yourself quite rich.

I got most of this information from this person's rather extensive post on GameFAQs. It includes quite a bit more information, including detailed descriptions of each processing interval.