Will 14.4 volts from my solar charge controller damage my 12v equipment?
This really does depend on the &quot;12V&quot; equipment.
If it's designed for automotive use, or motorhome/RV or marine use, it'll be designed with car batteries in mind, and generally tolerant of 15V or so while the battery's charging - as well as the sort of voltage spikes sometimes seen in a car.
Plus, DC motors used in pumps and such are pretty robust anyway.
If it was designed with a precision regulated 12V supply in mind ... maybe not.
Arduino should have a step-down regulator to 5V in the system so it should be fine (but if it's a linear regulator, it may get hotter and need a bigger heatsink)
So add a list of the specific equipment you have in mind, to the question, and hopefully you'll get a better answer. If some specific item is NOT so robust, a regulated supply should take care of that, leaving everything else on the battery.