Do I only have to connect the switch CPU to that vlan or do I have to add the vlan to the bridge as an interface as well?
Since you're bridging everything between the two switches, tags and all, then the bridge "gobbles up" the entire CPU interface of the switch - meaning that you now interact with the vlans via the bridge interface - so yes, if you want an IP address on the router on a management VLAN, then add a vlan sub-interface to the bridge interface, and set the mgt IP address on the vlan sub-interface.
And if there is wireless, that has to connect to a bridge correct?
Generally speaking, yes - for instance if you're making the WLAN clients be on the same network as the hard-wired LAN clients, you'll need to bridge the wlan interface.
I'm not sure if the wlan interface itself supports vlan tagging, but I know the VAPs do (virtual APs) so you could configure your SSID on a VAP instead of on the actual wlan interface, and then put whatever vlan tag on the VAP you wish - so you could very easily have multiple SSIDs which connect to various vlans. And yes, you would add the wlan1 interface to the main bridge, and just let the vlans reach the proper VAP interfaces via the tag - just the same way the IP packets reach the proper vlan sub-interface via their tags.