http://forum.mikrotik.com/t/using-routeros-to-vlan-your-network/126489/1
On the router side yes, vlans ( interface bridge vlan ) need to be tagged for bridge and for any trunk ports ( and hybrid ports)
When using bridge vlan filtering on switches aka 300 series, only the management vlan needs to be tagged on bridge.
NO, router management is not exposed on all vlans. Only the management vlan or trusted vlan can be used for router configuration etc.
If you are having issues its due to how one has incorrectly configured the router.