Learn Finnish: Asutko sinä täällä?

This is because of vowel harmony. The base verb is asua, which contains the back vowels a and u. Since the word contains back vowels, any ending attached to it must also use a back vowel. Therefore, we use -ko instead of the front-vowel version -kö.

How does adding -ko change the meaning of the verb?

The -ko (or -kö) ending is a question tag that turns a regular statement into a yes/no question. Asut means you live, so adding the tag makes asutko, which translates to do you live? In Finnish, the word carrying this question tag is usually placed at the very beginning of the sentence.

Is the word sinä (you) mandatory in this sentence?

No, it is optional. The verb asutko already has the -t ending right before the question tag, which means you (singular). You can completely drop sinä and just say Asutko täällä?. Keeping it in the sentence simply adds a little extra emphasis on the person.

Why does the word for here (täällä) end in -llä rather than -lla?