Learn Turkish: Rüzgâr çok şiddetli esse bile dağa tırmanmak istiyorlar. - Even if the wind blows very violently, they want to climb the mountain.

The verb stem is es- (to blow). Adding the conditional suffix -se gives us esse (if it blows). Following it with the word bile (even) creates the "even if" meaning. This -sA bile pattern is the standard way to form concessive conditionals in Turkish.

Could I use eserse bile instead of esse bile here?

Yes, you could. Esse bile uses the simple conditional (focusing on a hypothetical situation), while eserse bile adds the conditional to the aorist tense (focusing on a general possibility). In practice, both translate to "even if the wind blows" and native speakers use them interchangeably here.

Can I use da instead of bile in this sentence?

Absolutely. You can say esse de instead of esse bile. The structure verb + -sA de/da means the exact same thing as verb + -sA bile (even if). Note that you must use de here to follow vowel harmony with the front vowel in esse.

Why is dağ (mountain) in the dative case as dağa?

The verb tırmanmak (to climb) requires its object to take the dative case suffix -(y)a/e, because you are directing your action "to" or "towards" a destination. In Turkish, you literally say they want to climb "to the mountain".