first of all, update your openvpn,
www.openvpn.net/download
1)Can I use the same key for the two connections?
yes, is you enable that... but since you do not have password auth, you should not... just go make another cert/key.
2)Why is the tap adapter on the bridged connection not connected?
I dont know, i dont use bridges so im unable to support them (they are rarely needed)