Learn Polish: Dzięki empatii i zrozumieniu wspieramy się nawzajem. - Thanks to empathy and understanding, we support each other.

The word się can mean either "ourselves" (reflexive) or "each other" (reciprocal). While context usually makes it clear that we aren't just supporting ourselves individually, adding nawzajem explicitly highlights the mutual "each other" meaning and removes any possible doubt.

Could we use a form of jeden drugiego instead of nawzajem here?

You could, but it would be more complicated. Because the subject "we" is plural, you would need plural forms like jedni drugich (if the group includes men) or jedne drugie (for entirely female groups). Using the adverb nawzajem is much more common and convenient here because its form never changes.

Why do empatii and zrozumieniu have different endings if they are following the same preposition?

They belong to different noun genders, though both are correctly in the dative case. The preposition dzięki (thanks to) always requires the dative case. Empatia is a feminine noun, so its dative ending is -i. Zrozumienie is a neuter noun ending in -nie, which changes to -niu in the dative.

Does the position of nawzajem matter? Could it go before the verb?