Learn Finnish: Näettekö te meidät?

Meidät is the accusative form of me (we). When a personal pronoun is the object of an action - like being the people who are seen in this sentence - it takes this special accusative form ending in -t.

How does the word näettekö work to form a question?

It starts with näette, which means "you see" (plural or polite). Then, the question particle -kö is attached to the end to turn it into a yes/no question: "Do you see?". We use -kö instead of -ko because the vowels in the verb (ä and e) are front vowels, following vowel harmony rules.

Is it necessary to include the pronoun te?

No, it is optional. The verb ending -tte in näettekö already makes it clear that "you" (plural) is the subject. Saying Näettekö meidät? without the te is perfectly natural, though adding it can give a little extra emphasis.

I don't recognize the verb stem here. What is the dictionary form of näette?

The dictionary form is nähdä (to see). When conjugating this verb, the -hd- in the middle disappears to form the stem näe-. Then you just add the standard plural personal ending -tte.