Elementary school is effectively universal childcare. It's just you have to make it through the first several years first. Realistically that age is set to when children can be reliably self-sufficient enough that they don't require help with feeding / bathroom things.

At "basic" levels, yes, to all of those.

Here's a way to think of it: A society succeeds to the degree that it harnesses the maximum of each individual's potential.

The goal then is for a society to remove impediments that prevent someone from reaching their potential. Imagine a potential Einstein born to unfortunately poor parents. One measure of the how well these services are calibrated is the degree that that Einstein is able to reach their potential despite the misfortune of their parents.

Lack of early child care, eduction, transportation and certainly (non-cosmetic) dental care can certainly stifle someone's potential, so those seem like reasonable problems for a just society to aim to address.

You can already sort of see what direction this would go in with education. Just look at student loans. They're available to basically anybody, and as a result you see a growing industry of for-profit colleges and continually rising tuition even at established universities, as people figure out how to extract and siphon off the essentially unlimited free money from the government (actual source of money: the students' future selves).

This is what I would predict would happen with any UBI, more generally: it would just raise the prices of the things that people have to buy until all the money wound up with those who had the capital and the sophistication to capture it. It's not clear you'd even wind up with more of those things you listed, but it is certain you'd pay more for what you did get.