Learn Turkish: Adresi haritadan kontrol etseymiş, ormanda kaybolmazmış. - They say if he had checked the address on the map, he wouldn't have gotten lost in the forest.

kontrol etseymiş combines the conditional -se with the inferential -miş. If we used kontrol etseydi, it would be a simple past conditional meaning if he had checked. Adding -miş means the speaker is reporting this based on what someone else said, or deducing it after the fact (they say if he had checked...).

Why does the second half use kaybolmazmış instead of kaybolmazdı?

Because the first part (the condition) is reported with -miş, the result must match that mood. kaybolmazdı is the standard form meaning he would not have gotten lost, but kaybolmazmış makes the result reported too (they say he would not have gotten lost). The clauses in these types of sentences need to agree in their level of certainty.

Why does harita (map) take the -dan (from) suffix here? Shouldn't it be on the map?

In English, you check things on a map, but in Turkish, you conceptually pull information from a source. Therefore, harita takes the ablative suffix to become haritadan. You use this same logic when checking something on the internet (internetten).

Why does the sentence start with adresi instead of just adres?