Learn Turkish: Bugün nedense dağlara doğru haykırasım var. - For some reason today, I have an urge to shout towards the mountains.

It uses the structure you are learning in this lesson: the verb root haykır- (to shout/yell) + the urge suffix -ası + the 1st person possessive ending -m (my). Combined with var, it literally translates to 'my urge to shout exists,' which is how Turkish expresses a sudden or internal inclination to do something.

Could I use geldi instead of var in this sentence?

Yes! You could easily say haykırasım geldi. Both structures (-AsI + possessive + var / gelmek) express a spontaneous urge. Using geldi (came) emphasizes the sudden arrival of the feeling ('the urge to shout just came to me'), while var simply states that you currently have the urge.

How is nedense formed, and what does it mean here?

Nedense means 'for some reason.' It is formed by combining neden (reason/why) with the conditional suffix -se (if). It has become a fixed adverb, and it is very natural to pair it with the -AsI gelmek/var structure when you have a spontaneous feeling but aren't sure why it hit you.

Why does doğru follow dağlara? Doesn't doğru usually mean 'right' or 'true'?