Adding second Ground Bus to Square D Sub Panel - Grounded via wire or just the screws?
Follow the instructions.  You are obliged (NEC 110.3) to follow the extra grounding bar's instructions.  That's because those instructions are the basis for UL granting it a listing as safe. 

As long as you met the instructions, feel free to exceed. So you can add a ground wire even if it's not required.  Generally you don't downsize a service wire (i.e. you wouldn't run 14AWG to the last single 5-15 receptacle of a 20A circuit), so you'd stay with 5AWG Cu ground wire. 

Any type is fine, as long as it meets the original current rating.  So don't pay for 2' of 3-3-3-5 just to obtain 2' of #5, use #5 or #4 THHN instead if it's cheaper.