You probably don't need a pedal wrench - a narrow 15mm wrench will usually do.

Yes, it is something you can screw up, as the left side pedal screws in counter-clockwise (so it doesn't come off as you pedal). If you are careful, you can certainly do it.

Use white lithium grease - dirt cheap and a can lasts a LONG time. You just need enough grease to ease the threads in - a very small amount.