Learn Italian: Siamo qui insieme. - We are here together.

In Italian, subject pronouns like noi (we) are usually left out. Because the verb siamo is specifically the 'we' form of essere (to be), it already tells us exactly who the subject is. You would only add noi if you wanted to emphasize 'we' as opposed to someone else.

Since the subject is plural, shouldn't insieme change its ending to match?

No, insieme is an adverb meaning 'together'. Unlike adjectives, which describe nouns and must match their singular or plural forms, adverbs in Italian never change their endings. It will always be insieme no matter how many people are together.

I have also seen qua used for 'here'. Could I use that instead of qui?

Yes, you absolutely can. Both qui and qua mean 'here' and are often used interchangeably in everyday Italian. Qui can sometimes imply a more specific spot (right exactly here), while qua can mean a more general area around the speaker, but both work perfectly in this sentence.