You need a crank extractor to remove the cranks.



The 564 has a 68mm-wide bottom-bracket shell and I expect the spindle is about 115mm long (measure it end-to-end). So if my guess is correct, you'd shop for an English-threaded 68x115 bottom bracket (assuming you intend to re-use your Sport LX crankset). Shimano's UN-52 is a good all-around pick IMO.

Regarding headsets, it might use either a 26.6mm or 27.0mm crown-race diameter and I don't recall which one you'd have on a 564. This item also is best installed with the proper tools, so maybe you should buy it at the LBS and have them install it.

For brake hoods... those could be a tough one

On the chain, my vote goes to a Sachs PC-68. Sachs chains are strong and reliable, plus they're easy to put together with the included PowerLink. You'll still be needing a chain tool to shorten the chain.