Wow, I had to look up some of those codes since they are so rare. Here's my assessment of each:

P0446 - Most likely the gas cap is leaking or not seated correctly. Just went through this with our Nissan Altima. Very rare code to pop up.
P0441 - Most likely the gas cap is leaking or not seated correctly. Also very uncommon to have this code.
P0440 - Hmm, another gas vapor code? Have you checked or replaced your gas cap yet?

This would also explain the stumble you get on cold startup. The gas cap seals the fuel tank so when the lines are pressurized by the pump, they can't drain back out once you turn the engine off. The fuel lines will hold their pressure until you go to start again. If the gas cap is leaking then instead it allows air to enter the tank which allows the fuel lines to drain out. When you go to start in the morning, the pump has to not only purge the air but also build pressure again. It takes around 5-10 seconds for it to do this. That's most likely your stumble.

The P0300 (multiple cylinder misfire) is probably the engine sensing that the injectors are injecting air, not fuel at startup. Replace your gas cap and clear the codes, they should not come back.