"Every day he goes to a synagogue."
Translation:Кожний день він іде у синагогу.
Why is the uni-directional verb йти used here, even though this is a recurring action? I would have used ходити.
Both «іде» and «ходить» sounds OK here. If you use «іде», you just view every day separately, and in the context of that day, the action is unidirectional.
What is the difference between кожного дня, кожний день, and щодня?
All the options work. Speakers of different regions might have different preferences, but the meaning is basically the same.
For telling time, you can use either an adverb «щодня́», or you can use a noun phrase adverbially. The noun phrase can be used both in its accusative form (кожен день or кожний день) and in the genitive form (кожного дня). The accusative case has two forms, short one (кожен день) and long one (кожний день), and both work here.
Some people try to only use «щодня́» as an adverb, and not noun phrases. (However, noun phrases are still used in other contexts, i.e. «Коже́н/ко́жний де́нь прино́сить що́сь нове́» 'Each day brings something new' — here, «ко́жен де́нь» does an action of 'bringing', so it's not an adverb, it's a subject.). For example, this is suggested by an online style tool onlinecorrector.com.ua. However, I don't think this recommendation reflects the real usage.
@carbunkul Likewise. I suppose that construction will be introduced later. @Michael I think that would work. What puzzled me, though- I thought it was кожен день.