Two clauses can assign different cases
In Ich besuche den Nachbarn, dem du hilfst., the main verb makes den Nachbarn accusative. Inside the relative clause, helfen needs dative, so the pronoun is dem. Copying the main-clause ending would lose this distinction. Feminine dative is der; plural dative is denen.
Die Nachbarn, denen wir danken, wohnen oben.
The neighbours whom we thank live upstairs.
Keep the preposition with the pronoun
Use the case required by the preposition: mit takes dative and für takes accusative. The relative clause keeps its finite verb at the end. With a two-way preposition, decide whether its own phrase expresses location or a destination; an unrelated movement verb does not decide the case.
Das ist der Nachbar, mit dem ich jeden Morgen spreche.
That is the neighbour with whom I speak every morning.
Whose: look back to the owner
In die Nachbarin, deren Fahrrad hier steht, the owner is feminine. The neuter gender of Fahrrad does not change deren. A masculine or neuter owner needs dessen. Do not add another possessive determiner after either form.
Das ist der Nachbar, dessen Fahrrad ich benutze.
That is the neighbour whose bicycle I use.
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References
Original explanations and examples informed by grammar references. Level placement is an editorial teaching choice.