Learn German: Habt ihr beim Abendessen hier gesessen?

The infinitive is sitzen (to sit). Because it is an irregular (strong) verb, its past participle is formed with ge- at the beginning and -en at the end, rather than the regular -t. Notice that the vowel in the middle also changes from "i" to "e", making it gesessen.

Why do we use habt (haben) as the helping verb here instead of a form of sein?

In standard German, verbs that describe a stationary state of rest, like sitzen (to sit) or stehen (to stand), use haben. You generally only use sein (to be) for verbs that show movement from one place to another, like going or driving, or a change of state.

Where does the word beim come from?

beim is a common contraction of the preposition bei (at, by, during) and the word dem (the). Because Abendessen (dinner) is a neuter noun, its

Why is gesessen at the very end of the sentence?

This is the standard word order for the Perfekt (past) tense. The helping verb (Habt) takes the main verb slot—which is at the very beginning for a yes/no question—while the past participle (gesessen) gets pushed all the way to the end of the sentence.