A. You'll enter the Schengen zone in Finland. So you clear immigration there. There will be no immigration check in Lithuania.
As you are flying on a single ticket, your luggage will be checked through. You won't need to collect it in Finland. Just proceed to the transfer desk (clearing immigration along the way). You may need to go through a security screening again in Finland.
B. Airlines will very rarely check through luggage when traveling on separate tickets with separate airlines. This means that if you have checked baggage you will almost certainly need to collect and re-check them in Beijing. To do so you must clear immigration.
If you are traveling with carry-on only, you may be able to transfer without clearing immigration assuming you don't need to exit the international zone to change terminals (I'm not familiar enough with Beijing airport to speculate on the likelihood of this).