No, a megabyte for a png file is not big at all. The more pixels (resolution) your image has, the more information and a bigger file. Also bigger resolution makes longer rendering times. A jpg file is very lossy and that’s why it gets the file size down. With png you’re not losing any visible color information.
Final animation will be compressed with the video codec (mpeg-4 probably) which gets the best quality output if it starts with some sort of quality in the first place. Although the same might not be true for youtube converters.
Multilayer openEXR with many passes can easily go over 50 and 100 megabytes per frame, so a megabyte per frame is quite reasonable. EXR is very much needed in compositing. It saves all information, including information that’s not in the visible color range.
It takes a long time to render an animation. Best to use multiple computers or a renderfarm, such as http://raypump.com/