Searching "aliquot castra" I happen by luck to find an old article (Rand, Edward Kennard. "On a Passage in Virgil's First Eclogue." The Classical Journal 2.3 (1907): 125-128.). in which the issue at hand is mentioned (tersely unfortunately).
In that paper a passage from the Ecoluge is dealt. For our need however, the relevant line is:
Aliquot as an indefinite adjective is common and is very suitable for your purpose.
Here are some examples taken from archaic and classical authors:
Cato, orig. fr. 128 Peter: interim aliquot <p>au<ca> castra feci
Plaut. capt. 161: eorum sunt aliquot genera Pistorensium
Cic. Cluent. 168: dico illum [...] aliquot dies aegrotasse et ita
I think that here hoc is a anaphoric determiner pronoun which links to the declarative clause introduced by the so-called explicative ut. Cicero employs a similar construction (with the pronoun as the subject) also in de orat. 2,4:
sed fuit hoc in utroque eorum ut Crassus non tam existimari vellet non didicisse, quam [...]
Other examples with different ...
Yes, the nominative plural of axis is axes.
Mundi 'of the world' is the genitive singular of mundus 'world', and you probably wouldn't pluralize it in most contexts (presumably there's still only one world), but should it become necessary to do so, the genitive plural is mundorum 'of the worlds'.
Axes mundi reads correctly to me, for your purposes.
As Cairnavon already noted, for break, one can chose rumpo. In terms of sense I believe it is spot-on, but it also comes with a bonus: Latin has the idiomatic expression rumpe moras! literally means: break up delays! This is used by Virgil for example:
heia age, rumpe moras! (Come on! break up delay!); [Aen. 4:59]
So we might have something like:
If you're looking for a Latin translation of the common tech bro line "Move fast and break things", a very straightforward option would be:
Prōcēde vēlōciter et frange rēs.
Prōcēdō seemed like a better option than the obvious moveō, since nominally progressive motion seems to be implied, not just random stirring. I used a singular imperative; for ...