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3) What tech do you have?
If the enemy forces are still taking damage (rather than sweeping the whole thing each turn), then keep the mines coming.
Sats are great in combination with the mines, since you can cut apart the crippled ships as they come through the warppoint.
If you have the tech, include NullSpace sats; the enemies coming through the warp point start at point-blank range, so you can rip thier guts out on the first volley. Then, use normal weapons to finish them off.
Having a few long-range attack ships stationed in the sector would also be very useful, so you can chase down the enemies who survive the mines and sats. A ship with WMGs should be able to stay out of range of the enemy weapons while it cleans up.
Even better, if you have psychic tech try putting half a dozen or so (I usually use 8 at a time) medium sats with large mount allegiance subverters on them at the WPs. Nothing hurts your enemy more than capturing his ships intact! But beware that subverters don't have enough range to shoot at ship on the other side of the warp point (on the tactical combat map I mean), so once in a while enemy ships will slip through - you might want to have a ship or two near by as a backup. If you are playing humans with master-computers-controlled ships, you probably should add a few sats with virus packages on them. Currently you can capture a MC-controlled ship with subverters once the MC is destroyed.