You can get a maximum of 120 seals per company leve you do for higher leves (starting at level 40 but you can set the stars up to 5 for level 52 mobs), about half that for lower leves (starting at about 30 and going up to 42). They cost 1 leve allowance to do but you can do them on the fly whenever you want, you don't have to go get it from the adventurers guild beforehand. These can be easily spotted on your map with a leve icon at the camp. Just talk to the GC NPC there and tell him to sign you up. All company leves are solo content only. Others can heal and buff you but they cannot help you fight. You can also only take part in GC activities in your own region at the moment.

I don't remember how many seals you can get from chocobo escorts but it's more than for leves. You can easily solo the lower level (maybe level 30?) chocobo escorts at a higher level but the level 50 escorts are hard (if not impossible) to solo, you'd need a party of others in the same company as you to pull them off. These can also be done on the fly, no preparation needed, but it's only at certain times, like behests. Just hang around the camp and watch the NPC by the chocobos, he/she is likely to salute when it's time. Just talk to them and stay with the birds. If you're having a hard time doing this, try bringing along some gysahl greens, they'll heal the birds. They're common enough drops around Eorzea and you can also get them from failing the event (possibly from succeeding too, I don't recall).

I'm not sure which GC you're in but if it's the Maelstrom the locations you'll need are as follows:
Easy (level 30+) company leves are in Cas (can't remember how to spell the full name) Hollow, in the cave south of Bloodshore
Harder (level 40+) company leves are at Bald Knoll
Easy (level 30ish) chocobo escorts are at Bloodshore
Hard (party of level 50s only from the same GC) are at Skull Valley
If you're in a different GC, you'll have to research the locations yourself, but they should be easy enough to find.

Quests are great, make sure you do them all. That includes searching other locations for them. I found a Maelstrom seals awarding quest in Grid or Uldah (I don't remember which) a while back so keep your eyes open everywhere in the world.

More seal awarding content is due soon, let's cross our fingers it's next patch!