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You have a "Singer 15 Clone", made in Japan. If you search this site for "Singer 15 Clone" you'll find additional information and probably a link for a generic manual for these machines.
It will use a Class 15 bobbin, very common, and 15x1 needle, also very common. As to the slide plate I can't say for sure, but an actual Singer 15 slide plate may fit, or a slide plate from any other Clone would likely fit.
You should be able to sew with it just as it is on a flat surface (but oil will likely drip from the bottom). There are plans on the internet for making bases to hold loose machines.