Villagers are never too old to learn:

It's the nursing baby that is attending the school, not the mother. And you don't need a Scholar for that.

Note also that the mom is not pregnant; the baby was born and added one to the population. Now it is nursing until age 2.

What a shame! Here I thought my precious 'nursing mothers' finally had a another purpose, other than nursing their young. I am sooooo SAD.

You could see their purpose as carrying the baby to the school. Otherwise baby would have to wait until it could walk.

I have a teacher that will teach for a few minutes and then runs off and goes to farm or something. Can I make her stay, or do I have to keep bringing her back?

Have 4 or 5 teachers, they will take turns

I had the same thing happen to my nursing moms! I think it's cute that the moms take their kids to school, though I wish that the mothers could gain skills. Also I've noticed that some of my villagers are having babies at a very old age. One of them is 68 and nursing. Is this normal, or do the villagers in this game have better chances of having kids?

No, it is not uncommon to see women bearing children beyond the normal age in this game. See the thread I started earlier today entitled "Oldest Mom".

Hmmmm.............. how do I get the option to build the nursery/school?? I would think a building would be there to be built, but I haven't had that happen. Or, do I need to have a teacher first? Thanks for all your info here, I am loving the game (as always).

To be able to build the nursery, you must
Then, there will be a building (that doesn't look like the huts) that your villagers can start work on.