For the non blackened parts, try soaking for a day or so in vinegar.
I just save what's left over from a jar of pickled onions, and decant into a larger container.
Wash of the then softened, rust in hot soapy water with a fine wire brush; I use one of the little ones with stainless bristles, as they are even gentle on the hands.
N.B. use hot water and dry the part immediately on an old towel; that you used hot water assists here, as the last remains of the dampness will evaporate. The part will surface rust again in very few minutes.
Spray with WD40 or similar whilst still warm.
The procedure removes the rust, but still leaves a pleasant patina on an older item.
I've done this with various very rusty tools from car boot sales etc.
Even a solidly seized pair of pliers can be given a new lease of life with little effort or risk of damage.
Bill