Learn Finnish: Oletteko te tosissanne, kun ajatte varikolle? - Are you serious when you drive to the pit?

This is a subject-bound state adverbial. It comes from the word tosi (true). It is put into the plural inessive case (tosissa-, meaning "in the truths") and then takes the second-person plural possessive suffix -nne to match the subject te (you). So, olette tosissanne literally translates to "you are in your truths."

Would it be wrong to say oletteko te tosissaan?

Yes, that would be incorrect. When expressing a state like this, the possessive suffix on the adverbial must always match the subject. Since the subject is te (you, plural), the suffix must be -nne. The form tosissaan has a third-person suffix, so you would use it for "he/she is serious" (hän on tosissaan) or "they are serious" (he ovat tosissaan).

Why does varikolle use the -lle ending instead of the "into" ending -on (varikkoon)?

The word varikko (depot, pit, garage) is one of those places that conventionally takes the outer local cases (the "on/onto" cases like -lla, -lta, -lle) rather than the inner local cases (the "in/into" cases). So, driving "to the pit" is expressed as driving "onto the pit" (varikolle).

Could we drop the pronoun te and just say Oletteko tosissanne?