Learn Farsi: کلِ شهر را دیدیم.

In Farsi, کل acts like a noun meaning 'the whole' or 'the entirety.' Therefore, کلِ شهر literally translates to 'the entirety of the city.' The ezafe is required to link these two nouns together.

Could I use همه instead of کل for this sentence?

You could say همه‌ی شهر, but there is a helpful nuance here. کل is the best choice for singular nouns to mean 'the whole' or 'the entire' single unit. همه means 'all' and is much more commonly paired with plural nouns (like 'all the cities').

Why do we need the word را here?

The word را marks a specific direct object. Because you are talking about seeing a specific, completely defined thing ('the whole city') rather than just 'a city', you must place را immediately after the object to show what is being seen.

Is the sentence missing the word ما (we) at the beginning?

It is completely perfectly fine without it. In Farsi, subject pronouns are usually dropped because the verb ending already tells you who is doing the action. The -یم ending on دیدیم clearly means 'we saw.' Adding ما at the start would just add extra emphasis, as if saying 'We saw the whole city (and someone else did not)'.