On what basis must one pick one posek and follow his piskei din on ALL matters, for kula and for chumra? i.e. If you follow Rav Moshe, must you follow all his chumras too (i.e. no Shabbos clock for an air conditioner)? Why?
There is no such basis. Why do you assume there is any such rule?
However, one must make sure their actions are acceptable according to whom they asked, and can not pick and choose to get a hybrid din. The classic example of this is davening both Mincha & Ma’ariv between Plag & Shekia.