Most of modern mobile devices have a width equal to 320px (even when the real size is more than 320px, they rescale website to have 320px width), so most likely 320px should be sufficient width for logo.
As to icons: just estimate how much icons would you like to fit into 320px width. E.g. for 10 icons the size should be 32px at most (really less that 32px, because of possible paddings etc.).
MJ changes image format "on the fly" if mobile device doesn't support initial format. But most of devices support gif, jpg and png.
