When I have a second trade port does this increase the global delivery rate?
Yes you can - you can have any number of trade ports and trade depots in your city, and they will each sell your goods individually. This works especially well when you connect your trade ports to the rail network as the main obstacle you will have to overcome is the load on your road network from the delivery trucks.
The way that I have done this in the past, is to set up multiple trade ports (I had 4 of them) in a city with lots of coal being extracted using advanced coal mines, and raw ore being extracted using ore mines. These resources were smelted at multiple smelting plants, and the alloy and metals obtained from this process were then sold on via my trade ports.