For those small scratches, I would suggest you rub on and buff off some Old English Scratch Cover. My daughter was given some old end tables with scratches like that all over the tops, and I liberally doused it with the OESC, wiped it off with a soft cloth, and it was as if I had refinished it. The scratches had disappeared.

thanks! I'll look into that.

The finish is most likely varnish if denatured alcohol doesn't touch it.
I would remove the top, place it on a level surface and brush it all over with a mixture of 2/3 denatured alcohol and 1/3 lacquer thinner. Don't wipe just brush on so the finish is melted then allow to dry.
The reason for removing the top is so you don't drip on any other part.
Of course before you do this wipe with mineral spirits to remove any trace of wax or oil.
If that doesn't do what you want, repeat, upping the lacquer thinner content and wipe the old finish off with paper towels. Then apply a new finish, if you think it may get spills, use a poly urethane finish.

I'm not sure about this but you may want to ask if polyurethane finish would alter the tonal quality of the instrument. It would be awful if later you wished you hadn't done it.

A "not high end piano" is not like a Stradavaris violin. Laying some books on top will alter the tonal quality, as will a doily or scarf....but not so you can notice. Pianos are very often refinished without regard for the tonal quality other than not dripping stain or varnish on the strings.

And with the methods I suggest, the stain is not removed, so the color won't be much changed but for the removing the old yellowing finish.

Thanks. I think I'll see how far I can get with the scratch polish stuff, because it's a heck of a lot easier! :) Then we'll see if more steps are needed.

And as a matter of fact, it does currently have a scarf on it, a nice red dupatta that doesn't match anything!

The scratch cover helped quite a bit--I think I can wait before trying something that takes more effort.

But now it's time to address the piano bench. It's not the same wood as the piano and has aged differently. Not just the color, but the finish itself is smooth instead of crackled like on the piano. It might be solid instead of veneer. (Would that make the finish crackle less?) Do I just clean it up and let it be different? Put it somewhere else to be a seat and get my kid an adjustable stool so he can play properly?

(Yes, the piano is on wheels and single person can move it anywhere in the house easily. It even has grab handles on the back! No wonder it's out of tune again...)

Yep you're probably right. After doing some measuring and research (I don't play but I knew something was off) it turns out this piano's keys are about 5" higher than normal. The bench is normal. No wonder the kid has been standing up to play!

Wonder just how high those old stools go...and if they come in stripped down deco styling. :)

A bench is too short for most kids. When seated at the piano, the elbows should be just at or slightly higher than the top of the keys.
Those old whirling piano stools go pretty high....make a slip cover for it!
I suspect what you have is a studio upright. Shorter than an upright but taller than a spinnet.
Put a paisley shawl on the top of the piano....and maybe a vase full of peacock feathers on top as well ;-)

The bench is too short for adults! I've been looking at actual (new) adjustable benches and stools just to get an idea of the range and few come high enough for me to get my elbows right. (I'm short but still! My kid is shorter.)

A quick google gave me this dealer's ad on the same model (note the dealer saying it's child friendly. It isn't unless they stand! Also note the faded bench.):

http://www.chicagopianos.com/120409update2/hardman-minipiano.html

It's not a studio...might be a type of spinet. It's not at all normal. 38" tall, 18" deep (excluding the handles in the back that keep it off the wall a bit), 56" wide. The top of the keys are 34" from the floor. It looks like the one in the ad may be missing the casters. Might be something to look at next time I feel like flipping a piano over. Sure, it's a Minipiano, but it's still a piano!

Strange Piano!! Are there 8 octaves? I have a Baldwin spinnet about the same age...perhaps a bit newer. the keys are 25 inches from the floor and it's 36 inches high at the back. Strange....wonder how the works are different from a regular spinnet? the sounding board would be larger but the configuration of the hammers? Can't figure? And it doesn't appear to have any pedals?
You neet a tall bench....but then your kid won't be able to reach the pedals...if there are pedals!

Almost 8 octaves! And two pedals!

From what I understand, it was licensed off a Swedish oddity. There is a British version too (Eavestaff) and internet rumors indicate that the British one is a nightmare to service and the American one is okay. I'm a little scared to find out, to be honest. :)

The front panel opens and probably comes off for tuning. It doesn't sound that bad, surprisingly.