How do I setup NAT for multiple VLANs on different Subtnets?

Yes of course! Just set it up more like a switch aka no need for dhcp, firewall rules etc…
This should help with VLAN work… http://forum.mikrotik.com/t/using-routeros-to-vlan-your-network/126489/1
and also the pointers given at this post highlight the main points to consider for this Switch device.
http://forum.mikrotik.com/t/bridge-vlan-filtering/172864/2


For the original poster after rereading the thread, if being an intern in a company assigned to address MT products, then suggest this is really a good place to start…
https://mynetworktraining.com/

He often has sales/bundles for his courses.