1. Yes, you can pump the water from the sump to the lawn.
2. You shouldn't need to filter it if you have a good sump.
3. When you have the most water in the sump, you won't need to irrigate.
4. A sump pump will not provide enough pressure for a sprinkler system.
5. You can put an additional pump in the sump. You could use a shallow well jet pump and just drop the suction pipe with foot valve in the sump.
6. You will have to protect the pump by using a float switch to operate it.