Learn Turkish: Ana yoldan gitmeliyiz. - We should go by the main road.

In Turkish, ana (mother/main) acts as an adjective when it means 'main'. Because ana yol is an adjective-noun phrase rather than a noun-noun compound, it doesn't require the 3rd person possessive suffix -u that you would see in noun compounds like okul yolu (school road).

The suffix -dan usually means 'from'. How does it mean 'by' in this sentence?

The ablative case (-dan / -den) is also used to express the physical route or path taken to get somewhere. When paired with movement verbs, yoldan translates smoothly to 'by the road', 'via the road', or 'through the road'.

Is gitmeliyiz always translated as 'should', or can it also mean 'must'?

The -meli / -malı suffix covers both 'should' (strong advice) and 'must' (obligation). Turkish doesn't separate these concepts as strictly as English does, so the exact meaning depends purely on how urgent the situation is.

The verb root is git-. Why doesn't the t change to d here, like it does in gidiyorum?