I believe the two small holes are check dampers.
They would open into the area at exhaust outlet where draft is greatest, at stove connector collar.
Air rushes in from chimney draw, instead of drawing up through grates, slowing coal fire.
If they go under the top, into the exhaust path, next to outlet, when open they allow indoor air up the flue to cool flue gases, slowing draft. Thereby “checking” or slowing draft. They are not for wood use.
Without seeing grates, or shaker, I believe this is primarily coal. So overnight, these openings are opened to slow the fire, or when trying to prolong the fire for longer duration. Depending on chimney, they may need to be open to prevent overheating with a full firebox of coal.
A common trick was tilting lids to allow air into exhaust path with coal stoves when not cooking.
I have been firing a cottage heater coal stove along with wood burning cookstove the last two months and it only holds a fire overnight tilting the lid closest to exhaust outlet. This stove has a flat little “shelf” on the lid support edge that is the only way to keep top below 700f during normal operation. I can only close it fully while cooking, or rear burner plate goes over 800f easily. I get a dull glow of the center support between burners knowing lid needs to tilt. I have an oval damper at flue outlet, and round damper in pipe. Both closed runs .02 inches WC which reduces blue flame to almost none, but still overheats with lids closed.
Here is established coal fire;
![[Hearth.com] Washington Pet 8-19 Gray & Dudley, Nashville, Tn [Hearth.com] Washington Pet 8-19 Gray & Dudley, Nashville, Tn](https://www.hearth.com/talk/data/attachments/337/337109-5d9712050caa10e2569fd8627cfc8be6.jpg?hash=BtLuDAgdj0)
You can see the flat shelf at opening front to slide lid rearward, tilting lid.
Here is rear lid tilted, maintaining civil top temps;
![[Hearth.com] Washington Pet 8-19 Gray & Dudley, Nashville, Tn [Hearth.com] Washington Pet 8-19 Gray & Dudley, Nashville, Tn](https://www.hearth.com/talk/data/attachments/337/337110-e491ee09a026bbb327ede24941ddc380.jpg?hash=-74imMmP7I)