Learn French: Je vais démissionner. Tout le monde l'a deviné. - I am going to resign. Everyone guessed it.

It is the neuter object pronoun le, which drops its vowel before the verb a. Instead of replacing a specific noun, it replaces the entire previous statement: Je vais démissionner. In English, we do exactly the same thing when we say 'Everyone guessed it.'

Since l' is a direct object placed before the verb, shouldn't deviné have an agreement ending?

No. When the pronoun le replaces a whole clause or idea, it acts as a neuter pronoun and is treated as masculine singular by default. Because of this, the past participle deviné does not take an extra e or s.

Tout le monde means 'everyone'. Why is it followed by the singular verb a instead of the plural ont?

Even though tout le monde refers to multiple people in meaning, it literally translates to 'all the world.' Because monde (world) is a singular noun, it must take the singular il/elle verb form. This is a very common trap for English speakers!

Could I use the simple future and say Je démissionnerai instead of Je vais démissionner?

Yes, you could, but Je vais démissionner (the near future using aller + infinitive) sounds more natural here. French speakers prefer the near future for actions that are already firmly decided upon and feel immediate or certain.