Learn French: Lundi, je commence un nouveau projet. - Monday, I am starting a new project.

Because this sentence is about a specific, one-time event happening this upcoming Monday. In your current lesson, you learned that adding le makes it a recurring habit. If you said Le lundi, je commence..., it would mean you start a new project every Monday!

I want to say "On Monday", so why isn't there a word for "on" in the French sentence?

In French, you don't use a preposition before days of the week to say when something happens. To say "On Monday", you simply say Lundi. Never translate "on" directly by saying sur lundi!

Why is the translation "I am starting" when je commence normally means "I start"?

The French present tense covers both simple actions ("I start") and ongoing actions ("I am starting"). French speakers also frequently use the present tense to talk about things happening in the near future, just like we do in English when we say "I am starting a project on Monday."

I learned that French adjectives usually go after the noun. Why is it un nouveau projet instead of un projet nouveau?

You are right that most adjectives follow the noun in French! However, a small group of common adjectives describing Beauty, Age, Number, Goodness, and Size go before the noun. Nouveau (new) fits in this group, so it is placed right before projet.