Learn Hardcore German: In unserer Nachbarschaft helfen sich Mieter und Mieterinnen oft gegenseitig. - In our neighborhood tenants male and tenants female often help each other.

Because in is a two-way preposition. With location (where?), it takes the dative. Nachbarschaft is feminine, and the feminine dative of the possessive unser- is unserer. So: in unserer Nachbarschaft. With movement (where to?), you’d use the accusative: e.g., in unsere Nachbarschaft ziehen (people move into our neighborhood).

What case is sich here, and why can helfen use it?

It’s dative. The verb helfen always takes a dative object (jemandem helfen). In the reciprocal use, the dative reflexive pronoun stands for “each other”: Sie helfen sich = “They help each other.” Dative reflexive forms:

ich: mir
du: dir
er/sie/es: sich
wir: uns
ihr: euch
sie/Sie: sich

Do I need both sich and gegenseitig? Isn’t that redundant?