1. Yes, you can buy a ticket online and check in in transit

2. It gets kicked to problem/ holding bag area. If you are lucky, the airline that you buy ticket with may have time & staff in the basement to retag it to the new flight. Otherwise it would normally get sent on the next AY flight to HEL as a through checked bag. But may have some issues (as you are a no show on the AY flight, AY might decide not to accept it on the next flight as they don’t know where you are). Be prepared for some delays getting it to HEL