Learn Turkish: Eğer herhangi bir sorun çıkarsa, iade ücretsiz. - If any problem arises, return is free of charge.

Herhangi bir means 'any' or 'any whatsoever'. While bir sorun çıkarsa just means 'if a problem arises', adding herhangi emphasizes that this policy applies to absolutely any kind of problem.

Why is the word Eğer used here when the verb çıkarsa already has the 'if' suffix?

You are right that the -sa suffix in çıkarsa already means 'if'. The word eğer is grammatically optional, but Turkish speakers frequently put it at the beginning of conditional sentences to add emphasis and to signal early on that an 'if' statement is coming.

I learned that çıkmak means 'to go out' or 'to exit'. Why is it used for a problem here?

In Turkish, çıkmak is the standard verb used when problems, errors, or obstacles 'arise', 'emerge', or 'appear'. The combination sorun çıkmak is a very common pairing (collocation) you should memorize as a set phrase.

Can you break down the suffixes in çıkarsa?

It is the verb root çık- (to arise/go out) plus the aorist suffix -ar (showing a general or future possibility) plus the conditional suffix -sa (if). Using the aorist with the conditional like this (çık-ar-sa) creates a standard 'if X happens' structure for real possibilities.