^^^
There is no real specific size you must have it at, though ideally, it should be the default 800x600px(not absolutely necessary though). Pictures that aren't at this size will usually just be placed in loading screens as per normal, cept there'll be a black background in place of the missing space that isn't covered by the image. Signature, yes is basically your name somewhere on the work. Signature, name written, stamp, anything with your name, all signatures. Signing isn't necessary, but I suppose it helps prevent art theft, allows people to recognize you, etc.
Hope that made sense :c
Thanks Koto!