Hey Khan,
Ideally, I would recommend background image size of 2600×1500 pixels, since a sizeable fraction of Internet users have 2560×1440 px monitors these days. JPG is the best format in terms of file size and hence load speed, especially if you optimize and compress it slightly. In general, I would say that a single background image should not be much larger than 500 kB in size.
Regarding your second question – you can find the background resizing settings in “Appearance -> Background Slider”, “Size and position” tab ;)
Best,
Andrew | Satori Studio