The marked phrase is a sentence fragment. You shouldn't be troubled to find it in a script, as it happens frequently in speech. People don't always speak in complete sentences. (Know what I mean?)
The simplest fix would be to simply add a predicate to the fragment, making it a complete sentence:
My dreams are coming true. You and me are saving my lady ...
The two highlighted sentences are unrelated, so I don't think you can derive a definite common rule for both of them. They do both build on the context provided by previous sentences, which is why they can be understood by the casual listener—they could not reasonably be understood, if they were written on their own.
If you're looking for an explicit ...
The passive forms would be as follows:
TV watching is enjoyed by me.
Football playing is not liked by me.
But they sound so unusual that, outside of a mental exercise, nobody would ever actually use them.
There is no direct passive for the additional sentences. (Although a similar kind of translation might be made, it wouldn't be exact.)
Your examples 2. and 4. with the infinitival clause "to go out ..." are ungrammatical because the clause can't satisfy the complement requirements of "miss", which requires a gerund-participial clause as in 1. and 3.