Hello, SFgirl-- and welcome to English Forums.
'Like introduces a comparison that is expressed in a prepositional phrase;
as is employed as a conjunction introducing a subordinate clause.' -- That's the basic rule, yes, but
like is becoming more flexible and is accepted by many, especially informally, in the second function.
I don't understand your second rule about 'subjects' and 'actions'; I suspect it is the same as the first rule, since a prepositional phrase contains just an object noun (
He looks like an idiot) while a subordinate clause contains a verb--which usually expresses some sort of action-- as well (
I'll treat him as I would treat anyone).