No you're right, we'd normally stress vart and gått – it rarely makes sense to stress auxiliary verbs, except in some very special contexts of course.

Here's a lingot for reading my mind! It's not often that I'm so thrown by the pronunciation of the Text-to-speech that I think to ask about it.

vart = to where, while var = where. So you use vart whenever the action is going to a location. Sort of like how english has "who" and "whom".

English has largely dropped these directional words now, but var corresponds to where, vart corresponds to whither (to where), and varifrån corresponds to whence (from where). Equivalents in English and Swedish exist for here and there, too.

Who/whom is to do with cases, so: who is used like I, he, we, or they. Whom is used like me, him, us, or them. Whose is used like my, his, our, or their.

That would be much better as borde here.