Choose "fixed size" in the Marquee selection tool ribbon and set it to 720x720 (or 720xH for whatever your height is). Then place a selection on the canvas. Then drag it left or right until it centers (the center vertical line should show when it does).
When you do Automate -> Batch, you refer to a certain script (or "action" in the Photoshop parlance). Just make that action explicitly save the image the way you want.
Open a sample image.
Create a new action and start recording.
If you want to export in a certain profile, do Edit -> Convert to Profile explicitly.
Do File -> Save As...,...
Mostly it is about color temperature, white balance (they're not the exact same thing), contrast, and then using an HSL/HSV/HSB (Hue-Saturation-Luminance/Value/Brightness) tool to mute some colors, shift the hues of other colors, and emphasize other colors.