@LosDaddie,
1. I think the challenges end at 12 AM PST. So you should have five hours to get them all.
2. For the 4,000 cR challenge, I usually do campaign because it's more fun for me than playing four rounds of Gruntpocalypse.
3. For the other three challenges, multiteam is your best bet. The "No 'I' in Team," you have to get 6 assists in one match, is also easiest to get in multiteam: there's always plenty of action flying around, so you shouldn't have any problem; I got that challenge after two tries in two games of multiteam.
4. Yuppers.