English question: about the usage of the word remain

As yuri34 said, reamin is a copulative verb here, indicating the prolongation/persistence of the state, followed by an ed or ing participle as a predicative, such as job remained undone. But this predicative can also be an infinitive that has yet to be completed. In short, all the ingredients that can be used as slogans can be placed after remain, but the premise is that the meaning must be satisfied.

Your question about seated or seated is actually the result of not knowing the usage and seat of seat: seat is a special verb, which makes you sit down and be sat down (as distinguished from site down). Therefore, if an sb stays seated, it means "keep someone seated". If an sb stays seated, it must be used as an sb to keep SB(else/self) down, and someone makes someone sit down (and this is only possible in theory, just because it is grammatical and it is unlikely to appear in practical terms).

So, you can only choose to continue sitting.