Never saw if you got the seedling pictures you wanted. These are healthy and were planted in rapid rooter on 10/4. However the 2 on the right were not close enough to the light at first. (That light was always the perfect distance for all previous grows so maybe I need to replace the t5 bulb?) But those 2 on the right are too leggy they shouldn't be that tall. They were stretching to get to the light but they are healthy. The one on the left popped her head out today. The other 2 yesterday.
As you can see they are still in rapid rooters. They are fairly small as you can see from the upside down solo cups they are in. So no your pot is no where near to small. I water them with 12ml of water at bedtime. 6ml of water first thing in the morning and 3ml middle day. Depending on the environment you may need a little more or a little less water.
I plant them in peat pots like yours when the roots start growing out of the bottom of the rapid rooters. When I do I water the soil I'm going to use the day before potting them so it is moist and not wet. Immediately after getting them in the peat pot I add 12 ml water to the rapid rooter and leave the soil like it is.
After they are in peat pots I water when the soil is dry to my knuckle. Watch the top of the rapid rooter for clues as it will look bone dry when its time to water. However the soil deeper than knuckle depth should still be just barely moist. That's hard to determine but if it feels colder past knuckle depth but doesnt feel damp its probably just about right to water.
How much water you give them after that can be tricky in the size pot you have it in. That's what I use but maybe you should try one a bit smaller. A smaller starter pot you just water to run off. The bigger one I would water till the soil is moist but probably not until runoff until it has a decent set of larger leaves. Then you can water to runoff. To simplify watering when it is big enough go to a 1 gallon air pot or peat pot. Water to run off and use the knuckle depth test to determine when to water. When it outgrows that go to your final pot.
If those are really peat pots I plant pot and all when transplanting.
Use good soil. Fox Farms or one of the other ones recommended here but I can never remember the names.
That is not the only proper way to do it. It is just very easy and will help you figure out how to water a seedling.
As far as your current plant I really dont have a clue. But there is alot we dont know about it. Maybe someone else here does.
This is how small a ml is if you arent aware. The line is
30 ml.