- If I do so, I don't need transistors, right?
If you go with that last schematic with 8 port expander chips then no need for extra transistors.
- What kind of port do I need for this power supply
I have no idea what you mean by this.
- Is it possible to supply my arduino with it as well?
Would the external supply deliver 2.5A to each expander
No, the total current it can supply would be 2.5A and that includes your Arduino.
and would this circuit be parallel as well?
I am not sure what you mean but I guess no.
You do know you will only be able to get 7 colours from those RGB LEDs with that circuit don't you?