1. Which is long-term capability index or short-term as for CPK or PPK.

There is too much counfusion in such terms, I prefere within and overall variation estimates, as I readed:

ppk, cpk es short-term because uses within variation estimate and ppk uses overall variation estimate (overall = within + between), but as Jim said it can be taken the other way

2. why defined CPK is at least 1.33 and PPK is at least 1.67?

IMHO, to take in account unseen variation (that will happen the sooner or latter but not in the current data),

funny I think (look like Z shift <none sence>) but as qusys said, "the value must be determined by your customer"

3. is CPK value always less than PPK value when implementing SPC for calculating CPK & PPK on the same spreadsheet?

Wheeler said that it can be the other way if incorrect sampling is done, but as far as I know, cpk can be equal to ppk (if no between variation exists whithin variation = overall variation) or smaller

4. when do we calculate CPK or PPK during preparing PPAP package?

The experts said: "use cpk if the process is stable", others said that there is no process stable to perfection even on simulators. in advanced topics on SPC wheeler said not to calculate indicators if the process is not stable. ppk is recommended for initial studies.

IMHO, use something as somebody said "to manage, you have to measure", and ppk and cpk are just that, maybe not perfect but a way to measure the process behavior. Maybe your customer will tell wich one do he like, but question him about wich variation estimate uses, some use ppk and show it as cpk