Am I supposed to do all the lessons provided in one day?

Another way to determine whether to do lessons is to look at your Apprentice count. It’s a pretty good indication of how busy you’re gonna be.

Basically, take a fixed value for Apprentice (like 100), and never go over that. If you go over it, don’t do lessons until it goes below. If you are below the limit, you can do lessons up to the limit.
Later on, if you feel like you can handle more, you can up the limit. If it overwhelms you, you can lower that limit.

In general, I’ve heard that people who do this have a level-up time of about 8-9 days instead of the high speed 7, so it’s not even that much slower, and allows you to space things out very well.

This script even specifically caters to this type of levelling.