Learn French: Le chef a démissionné. Évidemment, je le sais. - The boss resigned. Obviously, I know it.

Here, le is a neuter pronoun that replaces the entire previous sentence: Le chef a démissionné. In English, we often just say 'I know', but French usually requires an object. So you say je le sais, which literally means 'I know it' (the fact that he resigned).

If multiple bosses resigned, would I change it to je les sais?

No, it stays je le sais. When replacing an entire clause or idea, you always use the singular, masculine form le. It acts as a neuter pronoun representing the whole situation, not the specific people involved.

Why use savoir here instead of connaître?

You use savoir because you are talking about knowing a fact or a piece of information. Connaître is used when you are familiar with a person, place, or thing. You could say je connais le chef (I know the boss), but here you are saying you know the fact that he resigned, so you must use savoir.

I see évidemment has two Ms. How is this adverb formed?

It comes from the adjective évident. French adjectives ending in -ent form their adverbs by replacing -ent with -emment. Note that even though it is spelled with an E, this ending is pronounced like 'ah-ment'.