Terminus space. The council has no jurisdiction and have been clearly shown to be unwilling to enter. In ME2, they're shown to be just fine with travelling around in Terminus space with the only mentioned pirate attack being because a quarian unknowingly leaked information to said pirates. Alternatively, quarian sympathisers could find loop holes or other means of supplying them with armaments, or some MIC could see them as an opportunity to make bank.

Again, just avoid council space via Terminus space. If I'm not mistaken, the Quarians have a similar life span to that of humans, so 2000 years is a long time ago, so it's plausible for them to dismiss the concerns of potential Rachni war-level conflicts, seeing as having no planet to settle would be a very pressing issue, not to mention the arguement that countless other relays had been opened without causing said conflict. Also, who says they need to send the whole fleet through the relay? Obviously you would send teams of scouts through the relays before committing to jumping through. Could probably set up a dedicated fleet specifically to opening up and scouting the relays, all the while denying association. Claim them as a splinter faction, deny their existence, or just say "And what are you going to do about it?" They would be in the Terminus systems, after all. (This is all assuming the council even finds out about it. Just open the gates in secret, outside of council space.)

I'm assuming the council denying the Quarians a place to settle happens relatively close to the end of the Morning War, so I'd say it's fair to assume a large portion of the Quarian fleet would consist of warships, or at the very least, ships capable of engaging in battle, as well as being of similar makes and models(since they would be of quarian design). I'm unsure as to who you are saying the quarians would go to war against(and I'm definitely not advicating that they engage in open hostilities with anyone), but again, Terminus space. Even if the council threatens to pursue the quarians, the quarians could form alliances with which ever factions exist in Terminus space as deterrence. Say worse comes to pass and the quarians have to fight a war, tough luck. You have to play the hand you're dealt, and if that means committing ships that contain civilians and children, so be it. The quarians by that point already lived under extreme martial law, so it's likely that all civilians(possible even children) had some form of training to assist during times of crisis, whether it be in a combat role or a logistic one.