Shimano 105 RD-5501 on a six speed freewheel? I was doing a cleanup at the storage room and found a box of mint 105 parts (brakes, FD, RD, triple crankset and BB). Based on the newspaper inside the box, the parts were laying there for at least 10 years.

I have a vintage Nishiki road bike with friction shifters and 6-speed freewheel and would like to upgrade it with 105 parts if possible.

I assume the brakes, BB and crankset should fit no problem. However, I'm a bit concerned whether the rear derailleur (Shimano 105 RD-5501) would work with friction shifters (SR Suntour, mounted on the frame)? And what speed freewheels might be compatible with it?

I don't have much experience with vintage bikes and parts so I hope you can help me out and tell me if my idea to upgrade the bike makes any sense?
Friction shifters do not care what kind of derailleur is at the other end and do not care about the number of speeds on your cassette or freewheel; they just pull the cable. So long as the shifter can pull enough cable to move the derailleur the appropriate range, everything is fine between the shifter and derailleur. 

So there's no compatibility issue with the shifter and the derailleur to be concerned about. 

The derailleur just needs to be able to move the range of the cassette/freewheel and clear it (depends on the maximum number of teeth, also how much chain it needs to take up depending on which chainrings/cogs you're in). A 6 speed freewheel should be fine; if you are to buy a new freewheel, in most cases a 7 speed freewheel would be the way to go; you may have to put a washer on for it to fit (but if you find a new 6 speed freewheel and want it for some reason, that's your choice). 

Edit: As Nathan points out in the comments, make sure to use a 9 speed chain (which should work with a 7 speed freewheel); the derailleur cage narrows as the # of speeds goes up, so you need a narrow enough chain.