I like all of these ideas!

I'm not sure about Permanence. Not having to defend your point, while if it's bot lane the enemy still has to defend theirs.

It'd really change things, not sure it's a downside, but it'd be really different. Especially if someone gets like a 1-2 minute permanence on top.

How would a warning work? By the time the 60 seconds have expired, the targeted points could have changed owner; on the other hand, knowing that in 60 seconds there will be a quest without knowing which points are affected is basically useless...

Not really it would just make champions with high survivability/escapes even stronger than they already are.

Before I start, remember that the quest system can go in several directions. It can simply be refined, or we can go a bit more crazy to involve more of the team on more portions of the map. Some ideas:
-A neutral, slow super minion spawns in the middle of a lane. Capturing it causes it to slowly move towards the opposing capture point. If it reaches the point, it will take the point for your team. Of course, the other team can capture it any time during its walk. Basically a tug of war.
-A "bomb" spawns somewhere on the map. Capturing it attaches the bomb to you, and if you manage to neutralize a point with it, it will remain your team's for a while (this one goes with the permanence concept). If you die with the bomb, it drops and someone else can capture it. You are revealed while holding the bomb.

Right, the general idea behind this is that it can change the map dynamics significantly, especially if coupled with a more free-form quest, not just the attack/defend one. It'd probably have the most impact in bottom lane.

If we don't do bottom-only quests, then "In 60 seconds, a quest will spawn." If no quest can spawn, then it simply won't. If we do, it simplifies matters greatly. The big impact here is that players will either try harder to gank or play very defensively.

Some of those quest ideas sound not like changes to Dominion, but like new game types/modified Dominion.

Honestly, if this were a game like UT 2K4, or for custom games, these could be fun to play now and then. Like when people would go "Capture the Flag" instead of "Deathmatch", but it sounds borderline like "Not Dominion".
Having such options, namely the super minion or the bomb sound like great things for customs.

Then again, "Dominion as is" is not something I'm sure is a sufficient "defence". After all, we are asking for Dominion to change, heh.

I'm all for new Quests in Dominion!

Perhaps get rid of the current quest system, which is currently somewhat random and, as stated, rewards the team who doesn't have windmill, and make the storm buff the quest instead. In other words, make only one buff spawn, which will be fought over by both teams.

Since it's a more contested objective now, the buff's duration can either be extended, or a much weaker version is granted to each surviving member of the winner team upon capture. The current quest buff is strong and can turn fights, but is very hard to notice compared to the PEW PEW LIGHTNING storm buff, so that's another plus.

This also ties into one of your other stated goals: making bot lane more interactive, since a strong bot laner coming middle to help will easily tip the balance in favor of his team, and it gives a "goal", of sorts, so all the endless ricefarming bottom eventually leads to stronger teamfighting.

i love these idears

while i agree that in general windmill quests do pose a great advantage, i think they should at least be kept in in one specific situation:
if my team is down by(say, 400-200), i think a windmill quest is a good balancer/a good way for my team to claw back into it. so, maybe windmill quests shouldnt be the first quest, but the second time a quest spawns, windmill should be an option.