'Kedden megyek dolgozni' is this wrong?
No, it is not wrong. It is emphasizing "kedden", instead of "dolgozni". Whichever is placed in front ot the verb is emphasized, usually.
Yup. Those two verbs are interchangable.
So is -ni used as a marker for some allative/lative case as well as the infinitive? Or is this supposed to be an infinitive?
-ni is the infinitive. But in Hungarian it is easier to learn verbs in the 3rd singular form, so that you learn the -ik verbs right away. Ő dolgozik, én dolgozom, megyünk dolgozni.
How would i put this sentence in hungarian if i intended "to work" to be a noun? Thats how i read it originally (ie, i go to the place that i work on tuesday) as opposed to work being an infinative and just meaning i go off to do work.
why "en dolgozni megyek kedden" is not accepted
Maybe because of "en". It should be "én".
What about: "Kedden dolgozni járok"?