Flight from Berlin to Beijing ( HU airline ) and then to Taoyuan -- Taipei ( Air China )

I will fly with Hainan Airline ( HU ) from Berlin - Tegel to Peking ( T 2 ) and 2 hours 10 min later with Air China ( CA ) to Taoyuan - Taipei ( via T 3 ) .

Questions :
1. Can I pick up my luggages at last airport ( Taoyuan - Taipei ) ?
2. Do I need to pass through Immigration and Re-Immigration in BJ?

Thanks !