Oven – How to clean the oven window

My guess:

With a little oven you probably don't preheat as long, and when you open the door you let ALL the hot air out. You need to reheat the air in the oven after the cookies go in for them to cook. Because the hot walls and rack are much smaller (and probably not as well heated to start with), it's harder for them to reheat the inside of the oven.

So the temperature is lower when you start the cookies. Some (maybe a lot) of the cooking time is spent getting the oven, the baking sheet and the air back up to temperature. Cooking them longer or at a slightly hotter temperature should help with this.

You're baking using a convection fan. This generally won't work unless the cake recipe is calibrated for it; you'll end up with a cake which is brown on the outside and raw in the middle (as you did). It's remotely possible that a combination of lowering the temperature and convection would be successful, but I don't have a formula for you.

Suggestions:

If the issue with top heat is that the cake is burning on top before the bottom is done, I would suggest placing a rack above the one the cake sits on, and a cookie sheet on that rack. This will protect the top of the cake from the radiant heat of the element, causing it to cook only from reflected heat off the sides of the oven. This may, however, increase cooking times somewhat so make sure to check cake doneness with a skewer.

Or: Add a baking stone on the rack holding the cake as well (under it), and preheat the stone for 30 min before baking the cake. This will give it some heat from the bottom.

Or: both of the above.

Or: get a new oven. They make fairly nice countertop ovens now which have a bottom baking element.