No, it's too small and will fall through the grates. I do have a customer that purchases 4 ton of nut and one ton rice. He throws a couple of shovel fulls of rice over the fire at night to dampen it off. Beside that there would be no use in a hand fired stove.
As far as your stove goes the three sizes listed largest first, Stove, Nut and Pea can be used. The smaller the coal the easier it is to control. Pea is about the size of quarter, Stove is about the size of baseball.
You can mix them as well, many of my customers use range which is mixture of pea and nut.