The proofs come from the Conquest boards. You can do more than one quest a day if someone shares it with you, but I'm careful to only open one of the reward boxes in a 24 hour period, as that seems to guarantee I get a proof.

Missions

Capture 9 different resources: if you can solo a resource, this can be done solo. It may take some practice to solo a resource as the guards can be nasty if you arent prepared. My general rule of thumb is to clear the tower first, then rush the flag, saving my ult for any players who show up. (PVE gear is fine for NPCs, but you'll struggle against defending players.)

Capture 3 different keeps: Either join a group or pay attention to zone chat and your map so you know when your alliance is attacking a keep. Rush there, and if you are in the tick zone, you'll get credit.

Kill 40 Players: do this one solo! Its very bugged for groups and you often won't get credit for your kills, but if you are solo, you get credit for enemies you damage. The best way I've found to do this quickly is by zergsurfing, especially if youbare new to Cyrodiil:
Open field fights: tag as many enemies as possible with some damage, even light attacks, and you'll get credit when they die.
Defending a keep: pour oil or use a meatbag catapult to defend the keep.

Capture All 3 Towns: this is difficult to do solo. The NPC flag guards are doable, but the towns often attract players, and one town will be on the far side of your map from your faction. If you do solo a town, be aware that the guards do respawn and can flip the flags back, so I always start at the unguarded flag to avoid NPC respawns.