If you work at a job you enjoy
This is actually two phrases. There's a that in here that's omitted.
If you work at a job that you enjoy.
So enjoy here is not an infinitive - it has a subject (you).
if you work at a job only to earn money
In this phrase, there's already a subject (you) and verb (work).
Earn doesn't have a subject because
only is ...
Generally, the question of whether to use the infinitive with "to" or the infinitive without "to" depends on the particular word (verb, adjective, noun) which commands the phrase, and you just have to learn that.
For example, modals, such as should, must, take an infinitive without "to", while verbs like ought, have (to) require the "to", even though they ...
The first is correct. "Tell" is in the infinitive mood. And you are effectively saying:
Now let's hear Marco (to) tell his story, except that idiomatically the to is elided.
Your second example uses the indicative mood of "tell" - but the sentence already has an indicative main verb - hear.
I want to write a book before I turn 40.
You're being direct and assertive.
I would like to write a book before I turn 40.
You're being polite or wishful, or implying "I would like to write a book before I turn 40 if possible".
I want to have written a book before I turn 40.
You're wanting some time to pass between you writing the book and you ...
As usual with question of this sort, the answer is 100% to do with the (unpredictable) properties of the particular word that governs the clause.
It happens that unaccusative verb prove (meaning turn out, be found to be) takes:
an adjectival complement, eg The mold on the plants proved benign.
a to-infinitve clause, eg The mold on the plants proved to ...
If an infinitive is preceded by an auxiliary verb and a phrase ending in do (such as What I did was, All we do is, etc.), the to is optional.
From Practical English Usage, 91.5:
Expressions like All I did was, What I do is, etc can be followed by an infinitive without to.
All I did was (to) give him a little push.
What a fire-door does is (to) ...
"Killing" is a noun (gerund) in this case. It's perfectly correct grammatically. It's a commonly used construction and quite familiar to me as a native speaker. In this case it means that Russia, Syria and Iran have killed a number of civilians, and that Mr Trump expects that the number killed will eventually be thousands.
I was on my way to simply up-...
In this case, to is part of the phrase on the way to, which is suggesting that the people he is talking about are engaged in a course of action that if unchecked could or will lead to multiple deaths.
If you wanted to make it easier to understand, you could rephrase it slightly:
... are, or are on the way to, ...
but regardless of one's opinion of ...
All of these are grammatically correct, though the first one would require a neologism.
In the first case, you're saying you've had nothing to eat, except something called "drink water". As far as I know, "drink water" isn't the name of a food, though I could see someone adopting it as the name for some sort of alcoholic water product ("drink" as a noun is ...
Not every "to" marks an infinitive:
on their way to the store
on their way to victory or defeat
on their way to doing something
This is the ordinary preposition "to". In general, it takes an object that serves as a destination or target. This may be more obvious when the object is a simple noun like "store" or "victory".
When the ...
To is a sign of the infinitive, but it's also a preposition. Since nouns are the objects of prepositions, gerunds (which take the place of nouns) can appear after to as well.
In the phrase the way to X, to has the meaning of destination. It's the same as saying "The destination of the way is X".
It's not incorrect to say to kill either.