If I use alternate state TEST in SHEET2, and pie and straight table in SHEET2 are in "inherited" state will the selection made in SHEET1 impact values on SHEET2?
With that setup the pie and the straight table on SHEET2 will not be impacted by selections on SHEET1 (provided the objects on SHEET on are not assigned to the alternate state TEST too).
You already mentioned a serious gotcha with regards to the $. Other things to keep in mind is that a number of functions like getselectedcount and getfieldselections cannot use alternate states, but always use the default state.
And see this discussion for some syntax examples for using alternate states with set analysis expressions.