How late can you fish on the river there?

I'm sorry I can't answer that question and be certain but if it were me basically the park is on one side of a public road and the river is on the over so in my opinion the river is not in the park.

It says the park closes at 8. My question is can you stay later than 8 and fish on the river where it goes through the park?

All state fishing regulations apply and, in addition, some waters may require special permits. Some lakes may also have restrictions on the hours they are open to angling and have more restrictive creel limits than state regulations. https://www.wichita.gov/ParkandRec/FishingandBoating/Pages/Fishing.aspx