My sump pit has water leaking into it, coming through the plastic wall. I circled the portion that has water coming through it in the picture below. I just noticed it's pumping water every few minutes but this is after we had a lot of rain. Is that normal?
looks like you have a hole in your pit liner. but its doing its job its still removing water from under the foundation as it should. however i advise you to call a reputable drain inspection service to do a video inspection of the footing drain those are the two pipes you see entering the pit. if water is leaking into the pit from a hole in the plastic liner it should also be coming into it from the two pipes that enter the pit.
This is completely normal and doing what it's supposed to: collect and discharge the water under your house. I'd say my sump runs about once every 3~6 hours, regardless. And as much as every half an hour or more during a good rain.
Obviously if you suspect foul play you should call the professionals at 1-800 GHOSTBUSTERS.