1. NPK? Same as TLC - a bit of fertiliser (Nitrogen, Phosphorus, Potash [yes,K!]).
2. Planting? There's folklore to cover every daily action, but it does help focus the mind. I'm not the potato guru, but I do it when:
a. The ground is prepared & workable - not claggy.
b. When the seed looks ready - with a bit of chitting. Some, like Pink Fir, are not ready with the others.
c. When I can work up the enthusiasm!!
d. 'Beating the gun' for anything at this time of year can only give you a marginal advance.