In Junos OS, as with many network operating systems, the control plane is responsible for processes that determine how to route traffic. This includes maintaining routing tables, which store information about network paths and protocols. Therefore, routing tables are indeed stored in the control plane.
Exception traffic refers to packets that cannot be processed by the normal fast-path processing of the Packet Forwarding Engine (PFE) in the forwarding plane, and thus are sent to the control plane for further processing. This might include packets destined for the router itself, packets that need to be fragmented, or packets that match certain firewall filter criteria, among other reasons.
Routing tables are not stored in the forwarding plane. However, the forwarding plane contains the forwarding table (sometimes referred to as the forwarding information base or FIB), which is a distilled version of the routing table optimized for fast packet forwarding. The forwarding plane uses this information to perform the actual transfer of packets across the network device interfaces.