Both fixed and singlespeed bikes only have one gear.
Singlespeed have a freewheel so you can stop pedaling and still keep moving.
Fixed don't have the freewheel, so you can't stop pedaling until you've stopped the bike.
With fixed the gear chosen is a compromise between being low enough to get up the hills, but not so low that you can't ride down them at a reasonable speed.
With singlespeed, you can freewheel down the hills, so the compromise is between low gears for up hills and going quick on the flat. This generally leads to a somewhat lower gear being selected.
I use 46x19 fixed, which is just about low enough for 10% on a longish hill, or 15% on a short one. It equates to 105rpm at 20 mph, which is quite adequate for making good progress on the flat. However I find that I can't pedal at more than about 160rpm for very long, so I have to use my brakes to keep below about 30mph going down hill.
As for knees, I don't think it does any damage so long as you get used to riding fixed, and riding up hills in a relatively high gear, over a decently long period.