If your space heater is gas or propane and is not VENTED to the outside via chimney or exhaust pipe, this will add humidity to the basement. You'll need a heater that can be vented outside or an electric space heater or electric baseboard.
You should close the 1 vent to the basement, especially if it is vented to the outside. Even if it vents to the upstairs, it is still a problem. The basement is cooler than the upstairs because it is protected by earth and soil. It does not get any warmth from the sun as the upstairs rooms do so it will always be cooler. The cool air attracts humidity from upstairs or outside and is the source of your moisture. Keep all doors and windows to the basement closed, both summer and winter.
Run a dehumidifier with a drain hose connected to your sump pump. It needs to be able to drain on its own, whenever it needs to. Get one with a built in deicer because it could freeze up in the cooler temperatures. This site about dehumidifiers
explains the idea.
The whole idea here is to isolate the air in the basement space from the outside or other areas in the home. Because the dehumidifier will have a limited amout of air volume to keep dry, it will automatically shut off when humidity levels drom to acceptable levels.
Your 95% humidity will attract mold and insects. I'd deal with this problem fairly quick if it were my home. Some people worry about running dehumidifiers because they use extra electricity but you'll find that the drier air is actually easier to heat so you'll save on your heating bills. Also, you'll find only 3 or 4 months in the year where the humidity levels are high enough to make it run more often. Right now, your humidity is high all the time because it has never been properly removed.