Cistern not filling up?

My en-suite toilet has developed a problem, I hope someone can help me with...
It fills up very slowly or not at all.
The water filling up in the cistern comes out like from a child's water pistol, so would take hours to fill the whole cistern. If I press my finger into the small hole in the "cap", onto what looks like a rubber washer, then sometimes the water comes out at normal speed and amount and it fills up fine, but then it goes back to the way it was again.

Also there must be a leak, as most of the time it doesn't fill up at all, or when it has filled up water drips into the toilet bowl and since this toilet is a macerator unit the pump starts and stops constantly, which is doubly annoying since it's next to my bedroom.

I've taken to flusher unit out and inspected it and it looks nearly brand new and I can't see anything wrong with it or how it works (but then obviously I'm not an expert).

Does anyone have any ideas how I can fix these issues?

Thanks!