"Turned it on " is correct. "I’m looking for them" is correct. She’s taken off her boots/ taken her boots off? Note that "She's" is a contraction for "She is" not "She has" . Therefore "She's" is not actually proper usage, however, it is common to see it used for "She has". Anyway, both taken off her boots and taken her boots off are correct.

Separable and inseparable are opposites. I have rarely heard the word "separable" used, but it could be used to describe that two objects are "separable" even though they are usually attached to each other. The word "inseparable" is usually used to suggest that two people are always together. My wife and I are inseparable. My daughter and her girlfriend are inseparable.

Basically, you just have to learn these as you go. There are no hints in the phrasal verb itself. For example, "turn on the light" can also be "turn the light on". But if you use "it", then the pronoun must go in the middle: "turn it on". "Turn on HIM/HER" means someone was attacked by an ally! "Suddenly, the family dog turned on me." (attacked me) "Look for..." doesn't separate. "Taken off her boots" and "Taken her boots off" are both correct. However, if the object is unreasonably long or has extra clauses, then it cannot go in the middle. "She had taken the boots that she bought earlier that day and continued to wear for the last few hours off" is just confusing, and incorrect.