I had been thinking of a possibility where "it" is used as a referential pronoun, and more specifically where it refers to some subset of a larger entity--in that case, having "all of it" or "it all" under control would be referring to the subset, and not to the whole. But granted that in actual usage, as an answer to a specific question, the question would likely clarify what is being asked about (i.e. whether it's the subset or the whole), and so in that case, either answering with "everything" or "it all / all of it" would be the same meaning.
But "all of (set of entities)" would more likely be used than "every___" for referring to a subset: after all, "everything" does not specify the restriction (other than whether is a "thing," person ("body"), place ("where")), but "all of (set of entities)" does specify it. E.g. "Did your classmates come to your wedding?" answered with "Yes, in fact all of them were able to make it." would refer only to "your classmates" coming, whereas answering with "Yes, in fact everybody was able to make it" would, with stress on "everybody," possibly refer to a superset of entities.
I think the expression is very simple and clear:
You have a break down in your car, a tyre puncture.
Someone stops and ask you:
- ¿Puedo ayudarte? (Can I help you?)
- No, gracias, lo tengo todo bajo control.
You have controlled the situation, you know what to do, you have all needed tools, and this isn't the first time you do it. You know very well how to it.
According to Google Translate: 'Bajo' can be used as an adjective, (e.g., low, lower, short), an adverb, (e.g., low, down, below, lower), a preposition, (e.g., under, underneath, beneath); or a noun (e.g., depth, bottom), whereas 'debajo de' is a preposition and means "underneath, beneath, or below". (These lists are not all-inclusive.)
I am a native English speaker, but I believe the most frequent usages of 'bajo' are as an adjective and 'debajo de' as the preposition. Examples that come to mind: La mesa es baja (the table is low/short); el gato esta debajo de la mesa (the cat is underneath the table). Note that 'debajo de' does not change with gender, but 'bajo' does.
Yes, there is a difference. Except in some archaic forms and idioms, verbs derived from haber are not used in the sense of showing possession, but act as auxiliaries in the formation of compound tenses such as the present perfect and past perfect, as well as providing the impersonal hay and habia (there is, there are, there were, etc. )
There is also a usage for showing obligation similar to "tener que" ( He de irme = I have to go) and probability (Mis llaves han de estar aqui =My keys have to be here) others, but I don't believe haber derivatives apply in this case. .