I think J-P is just exclaiming at how interesting is this aspect of word order in Magyar. It occurs to me that the examples may have other nuance(s) depending on context, such as where "akarni" could, would, or should be interpreted to mean "to demand", rather than "to want". Or, as BeaTth notes (below): "'. . . akarok menni' is 'I want to go (THERE)'"( which invokes a different "emphasis" than "I do want . . . .") [I hope that my comment encompasses J-P's probable inquiry.]
akarok translates to want - with this verb you express your desires. when asking others for something, e.g. when ordering at a restaurant, you might prefer using kérek, which would translate more to wish or wish for. E.g. "Vizet akarok" means "I want water.", "Vizet kérek" means something like "Please give me / bring me water". In this sentence, however, you are not ordering anything, so it wouldn't make any sense to say anything else than "akarok".
I am just beginning to study Hungarian and am no expert by any means. But I believe that the infinitive form in Hungarian does end in "-i" from everything that I have seen.
If someone more familiar with Hungarian would like to correct me, I am curious to know if that is correct as well
So yes, the infinitive is always "-ni" like: menni (to go), enni (to eat), inni (to drink)
The n is rather confusingly doubles here, because the root is so short :)
It is not the case with longer verbs though: aludni (to sleep), gondolni (to think), tanulni (to study)