"I go to work on Tuesday."
Translation:Kedden dolgozni megyek.
No, it is not wrong. It is emphasizing "kedden", instead of "dolgozni". Whichever is placed in front ot the verb is emphasized, usually.
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.