Atmega328 and Servo on same suppply
1) You can probably get away with powering the servos directly from the battery pack. 4x AA cells nominal voltage is 4 * 1.5 = 6V. (You probably measured 6.5 V on the batteries without any load. This is not the right way to measure battery voltage.) Edit: Use a buck-boost converter for the 5 V logic supply.

2) Go with a ground plane and put the servo ground connection as close to the battery ground as possible. Same goes for the servo positive supply. The regulator will deal with the voltage drop.

3) Use the recommended values from the datasheet for the regulator and ICs in your design. Keep loops tight, so put capacitors as close to the pins as you can.

I hope this helps!