Difference between "besides", "apart from" and "except for". Prepositions vs adverbials

I am studying discourse markers and ended up checking online (in crownacademyenglish) about the difference between these expressions.

Firstly, this website affirms that they are prepositions, which I disagree with. They can also be adverbials. Secondly, I am not sure I agree with the difference in meaning it suggests. I would like you to confirm my doubts with examples, if possible. Also, to show if, in fact, it is their word type that could produce such a difference in meaning in some contexts.

The text states that besides adds something to the clause. It means "plus".
Except (of) means minus; it has a meaning of excluding something.
Apart from is a combination of the two, meaning plus / minus depending on the context.

So, basically what I’m hearing is that a sentence like

• Next week, I’ll be in London every day besides Monday

is incorrect. Is this so?

Perhaps I am wrongly influenced by their equivalent expressions in Spanish, but to me, they mean basically the same.

To add something to the post, this is the definition of besides in an online dictionary:

As an adverb:

• Meaning moreover; furthermore; also: "Besides, I promised her we would come."
• Meaning in addition: "There are three elm trees and two maples besides".
• Meaning otherwise; else: "They had a roof over their heads but not much besides."

As a preposition:

• Meaning over and above; in addition to: "Besides a mother he has a sister to support."
• Meaning other than; except: "There’s no one here besides Bill and me."

Is there something I am not grasping? Thanks.