In High School how many innings can a pitcher throw in a week. What are the rest time and when does the week begin and end.

NFHS (FED) rules do not specify limitations on pitching. That is a league or association matter.

Well, it's really a State matter, unless the State has passed the responsibility down to a lower level.

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Ca. it's 10 per week, sunday thru Sunday. I'm not sure of a rest rule......

This is a state by state regulation. In Michigan, a player may not pitch more than three consecutive days regardless of the outs pitched; and a player may not pitch for two calendar days following that in which he pitched his 30th out. A student may participate in no more than two games per school day.
Coaches are supposed to exchange pitching data with opposing coaches before each game, but that seldom happens.
Bottom line is following the 30th out in any sequence which does not include a two-day rest period, a player may not pitch for two calendar days.