From what I see, it looks well worth refinishing! The drawers are made with solid woods, which is very rare now days unless you spend a fortune. I do not know woods (my husband might know but he is downstairs), but it looks like a very solid piece of furniture, like what used to be made before all this mass production got started. Is that last photo the back of the dresser? If so, again it looks like wood and not heavy cardboard, which sadly a lot of the furniture makers and companies have gone to. For refinishing, you will have to get someone else to help you. My hubby and I are going to refinish two vintage dressers, one is 42 years old and the other, 43! I know they have to be sanded and my husband has already started making repairs before we start that process. I will be learning as we do this!

Are the knobs made out of the same wood? Since the handles on both of our dressers are metal, we are cleaning them, after removing them, and spray painting them with metallic paint. They even look better than new now!

The knobs are like a hard material. And translucent but colored

I know exactly the type of knobs you are referring to. If it were me, I would replace them, especially if you decide to refinish the dresser. There are so many varieties and colors of handles and knobs out there.

the inner drawers are made from ribbon mahogany. the outside drawer panels are a veneer of crotch flame mahogany (veneer is a thin solid wood glued to a cheaper piece of wood). most of these dressers from this era used mahogany on the inner drawers. I've redone many of these.

if you've never refinished wood before, you should do some research. you have some deep scratches that will need fixing. the top will need to be stripped, sanded and stained, and a new top coat. (if you don't sand too much, you can skip the staining part. mahogany loves linseed or tung oil. it really brings out the color)

Is it worth anything? not really. looks like it's from the 40's, maybe late 30's, like these:

here's one that was painted black on the sides and trim pieces.

yes, I'd get new knobs. Hobby lobby has some nice ones. if you want to see what was on yours originally, prob something like these below, or above. :

i have a slew of these original hardware. they aren't expensive. check etsy or ebay for 'mahogany chest of drawer pulls', or 'lion head brass pulls'.

found one w/wood knobs too

Could the knobs be bakelite?