2010 Honda Civic Shake and stall

The AC might be it's own issue and need a refrigerant re-charge. That is about the only thing other than a temp probe sensor failure which is extremely rare.
The shaking at idle and stalling might be a vacuum leak. I say this because you describe the last stall happening when you took your foot off the brake which affects vacuum. Listen for vacuum leaks under the hood and get s piece of string to drag around areas near the intake to check for leaks.
If you don't find any, I suggest having the codes pulled and having the fuel pressure checked.
You can get the codes pulled for free at any Advance Auto or Auto Zone. It should not cost but about a half hour of labor to get your fuel pressure checked.

Hat sounds like the battery is low. You might be looking for a wiring problem. This gets a lot more involved as you will have to get a multi-meter and start looking for bad gorunds or shorts.
Let me know what size engine you have and I can give you the location of the ground points so you can check those.
In the mean time have the battery checked.