Power supply for robotics project?
Can I use a 6v regulator for breakout without any issues?


Well, with motors, I would reccomend against it. The motors (Especially if under load) will draw loads of current, and that will have to pass through the regulator, which will cause it to get very hot, as the effeciency of linear regulators is quite low. I would only really reccomend regulators in projects that aren't current intensive.


  And also I see people use capacitors alongside regulators to reduce spikes or something but I did not know what to implement so could someone explain that as well?


There are two types of capacitorrs that you may be referring to. Brown-out Capacitors will protect your circuits from brown out from using too much power, typically store enough energy for 1-10ms of operation. Pi capacitors are used to filter out induction spikes, and I would not be surprised to see them on the breakout board already.


  powering the arduino with a 12v 250mA source


Would reccomend against this. The arduino itself uses 45mA of current, which isn't a problem. What will be though, is the motors, which have to run on 205mA total. I would reccomend a 20A or higher suppply to properly power a decent motor, and an extra 5A for each motor thereafter.