Quests are short (up to an hour?) excursions through the Sentinel Gate, with a huge variety of purposes.
There have been quests to meet up with and discuss stuff with an NPC, quests to capture things, quests to rescue people/things, quests to get to X and do a ritual there, quests to kill stuff, quests to rescue stuff…
When the Druj sacked Dawnguard, a load of PCs from there were trapped in that territory, surrounded by Druj, fighting their way out. A quest was sent ion to bring them to Anvil.
A quest to recapture a chest of loot being carried away slowly by Grendel.
A quest to manifest (by means of big noisy things) and then purge (kill) gremlins in the mana mines of Urizen (kiddie linear, quite dangerous for the monsters)
In order to get onto a quest, be ready and willing in the central areas of your nation, prepared to go at short notice, and listen to your Egregore/Senators/Archmagi. Who may well come into the nation saying things like:
“An opportunity has arisen and we need Sentinels, Battlemagi, a fistful of crystal mana and a bottle of gin…”
“We’re sending a delegation through the gate to X, we need diplomats and bodyguards”
and that old favourite:
“Someone! Anyone! We need more bodies at the Sentinel Gate NOW!”
Note that while some quests may be one nation (maybe a dozen PCs), quite a few are combined expeditions (2 dozen PCs?), especially the Skirmishes (which tend to be combat heavy larger quests, with a good 50 or so players).
Danger goes the whole spectrum, and is altered by how prepared/competant the players are, and the level of opposition. Just myself, I’ve been on a quest where we (contingent of Dawnish knights) went to raid a Druj fort, and found it heavily manned and holding an Ogre. We retreated but lost 2 PCs. I’ve been on ones where the biggest challenge was getting the knights to run. And I luckily avoided one where about 50 knights went in, and 15 came back, cut to pieces by skilled and tough opponents.
Doing a lot of questing will get you a reputation as a reliable and effective battlemage. You may well get some loot, you may well get interesting rewards, and you will certainly make friends. Battle mage is probably helpful, but I don’t think ritual lore is. Personally I’d go for extra fortitude, endurance, and personal mana.