A wider pipe will cause it to drain faster, as will an altitude drop as Martin Sojka suggests. Not sure which will be more effective; if you do both it should drain pretty fast. I know when I was building a waterfall in my dining room, it tended to back up sometimes when the drainage to the caverns was only 1 square.
You can connect any number of things to a single lever or pressure plate. There is no limit (well, no meaningful limit, probably if you try to connect more than 65k things it gets confused). So feel free to go wild with that.
Since you're fiddling with drainage systems, I'll give you another bit of advice for free: especially if you build a wide drainage pipe, put in some vertical bars blocking the outflow, with some convenient stairs up right in front of them. Otherwise, Urist McMason will decide that he just absolutely needs to use a rock left behind when you were digging out the sewers, and if there's any way he can find to get there, he'll go charging down to grab it and get washed away by the current. Give him something to hit before he gets washed entirely off. I had this happen to me with my waterfall as well; the poor guy got washed out the sewers, down the 6 z-level drop to the floor of the first cavern.
Goblins normally follow their squad captain, if he is alive, unless there's a dwarf within about 20 squares. Squad captains normally charge your base if they can find a path, trapped or not, to a dwarf, and their squads follow. (Note: the previous answer is incorrect; goblins are just as omniscient as you are, except they can't see traps.) However, a known bug right now is that goblins with flying mounts sometimes get confused and have a hard time pathing; this especially affects captains because they're mounted more often than the normal troops. If the captain's mount is confused, his squaddies will just stand around guarding him, rather than attacking on their own. This is similar to the problem that causes attackers to hang around your entrance rather than heading farther in: their captain is caught in a cage trap, but he's not dead so they just stand around rather than leaving him behind.
How to diagnose this: First, find the goblin captain on the units screen. He's the one marked "Elite" or "Master", and he'll probably have a different weapon from his squaddies. Zoom to the creature, and see if he's inexplicably floating above the world, especially if he's above a tree or something. If so, you'll have to order the militia out there, because that's the only way you're going to get rid of them; and you'll have to gain some height so that your marksdwarves can shoot at the captain, remembering that they can't shoot upward. You might have to build a small tower nearby to arrange this. An goblin master bowman stuck atop a tree with no higher ground nearby is a deadly threat, almost impossible to get rid of, because he shoots any of your masons who try to build a tower for the marksdwarves to stand on (and master bowmen are ridiculously dangerous).
If the captain's just parked on the ground, with his buddies, and not attacking you, something else is wrong: probably there isn't actually any way into your fortress. Check the doors; besieging goblins won't path through locked doors or raised drawbridges. Trolls path TO these obstacles because they're building destroyers and they like to destroy them, but goblins care only for dwarves. So go ahead and open the gates. Just make sure the militia is standing behind, and your civilians are burrow-restricted not to go outside, &c.
Best Answer
A screenshot or rendition of the specific layout might be helpful, but I'll give answering a try anyway.
There are essentially two options for closing the tunnel. If you can drain it completely, at least for a while, you can simply construct a wall, door or floodgate to seal it completely, or fortifications, a grate, vertical bars or a statue if you need to let water through.
A second, more involved option, but that doesn't require draining the tunnel first is applying magma to the opening, turning the whole thing into obsidian, but that won't let water through (although fortifications can be carved into it at a later point).
Edit: Another option is to floor over any access points to the tunnel, on either side.