Overcoming voltage drop in a battery
For simplicity you could power the Arduino from a 5V low-drop-out regulator. You'd bypass the normal regulator (it isn't low drop-out) and get more usage from the 7V battery. I don't know what current is required by the uno so I can't definitely recommend something but maybe a 1A LDO like the L4941 would suit. It drops 450 mV at 1A and this means your battery can droop down to 5.45V before things go out of spec. You might need a heatsink - it all depends on how much the uno takes.

Or you could go the whole hog and have a buck-boost regulator like this one: -



This takes any voltage from 2.7V to 15V and gives you 5V and up to 2.5A. Or maybe just a buck regulator would suit. This one will work down to an input voltage of 5.5V and still give 5V out at 2.5A:-