Learn Croatian: Sudjeluješ li u zajednici? - Do you participate in the community?

Exactly! This is an -ovati verb. In the present tense, verbs ending in -ovati drop that ending and add -uj- before the personal endings (-em, -eš, -e, etc.). So, sudjelovati drops -ovati and adds -uješ to become sudjeluješ (you participate).

What is the base form of zajednici and what case is used here?

The base form is zajednica (community). The preposition u (in) requires the Locative case here because it describes where the participation is happening. For feminine nouns ending in -a, the Locative ending is -i, which is why it changes to u zajednici.

Could I ask this question using da li instead?

Yes, you could say Da li sudjeluješ u zajednici?. Both forms are used for yes/no questions. However, putting the verb first followed by the particle li (Sudjeluješ li...) is considered more standard and natural in written Croatian.

Is there a trick to remembering the word sudjelovati?