You seem to be getting ahead of yourself and you are making up all sorts of things that do not exist.

1.There is not grammatical relation between mood and preposition: the mood does not point to any particular preposition and vice versa; do not confuse preposition and conjunctive locutions; when it comes to those, yes, there is a dependence of the mood on the locution.

2.You write « [I have chosen {to} take this route.] », as if “to” were optional; it’s not, I do not understand what you are driving at.
Anyway the translation of the French is “I choose to take this route” and “I choose this route.”. Moreover there is no such “de” dropping rule, let me tell you, that’s complete gibberish. If you remove preposition and verb you do get a correct sentence that can be taken to mean the same thing, but yet, that is so only sometimes.

3.”je viens de me réveiller.”, in English is simply “I just woke up.”; you write “I have just {to} woken self up.” and that’s nothing in English; you must also be a student of English, no English speaker would write such things.

4.No, “Viens [a] vivre avec moi en France.” is not correct; there is never the item “a” there.

5.CONCLUSION: You’d better tighten up, you’ve got a lot of studying to do!