Dimming 6x large LED 8 segment blue displays
1) You need a bypass capacitor whenever you expect the voltage to drop suddenly (usually by large transistors or by lots of small transistors being switched on and off) Since you are switching LED's on and off, Yes you do need bypass capacitors on each IC. This is because each piece of copper also has a few uH-nH (depeding on size/width) of inductance so each IC is really a dynamic load and turns your power system into a filter.

2) Dimming could be accomplished by either controlling the LED switch voltage (assuming the  UND2981 can handle a wide range of voltage on VCC look that up in the datasheet OR dimming is usually accomplished via PWM, just google "PWM led"