Would this 6V battery be ok to run arduino from connected to the dc input? Or is 6 volts too much?
6V is kinda funny - little too high to run into the 5V pin directly, not quite high enough for the onboard regulator to regulate to 5V.
Go to www.pololu.com and look at their regulators, I think you can find one that will take 6V and can be set give 5V out.
6V is too high for direct connection to the chip. At this sort of difference you will be better off using a switching regulator like:-