Il est un travailleur extrêmement professionnel.
Il travaille extrêmement dur. (no “e”)

Rien à redire sur la place de l’adverbe, dans ces deux phrases : il est placé devant l’adjectif qu’il qualifie.
Par contre dans ce genre de phrase il faut employer le pronom personnel “ce” (et pas il/elle).

In these two sentences the place of the adverb “extrêmement” is fine, it comes in front of the adjective it modifies. But you should use the demonstrative form “ce” to refer to a specific individual, as you’re qualifying him

Il y a bien des règles qui régissent la place de l’adverbe dans la phrase, mais comme tu le dis justement dans ton commentaire il y a des exceptions.

Je pense qu’une règle générale serait de dire qu’un adverbe qui modifie un adjectif ou un autre adverbe précède ce mot et quand il modifie un verbe il se place presque toujours après ce verbe (mais pas forcément juste après).

Ici un assez bon aperçu de ces règles. Comme tu peux le voir les règles disent parfois “toujours”, parfois “presque toujours” et parfois la place dépend ….

Cette page me semble bien faite et peut-être plus accessible et en faisant les exercices ça te permettra de mieux intégrer les règles.

As you say there are rules and exceptions to these rules. In general we can say when an adverb modifies an adjective or another adverb it is placed in front of it. When it modifies a verb is is usually placed after the verb (after the auxiliary in compound tenses). But this is only general, it can depend on what you want to convey or on the adverb itself.

I think this page is a good overview of how to place adverbs in French. And this one seems good as well, with exercises if you want to train.

First of all “Il est un travailleur extrêmement professionnel”, although syntactically correct, is not expected in french.

I would expect “C’est un travailleur extrêmement professionnel”, or “Il travaille extrêmement professionnellement”. Don’t ask me why, it is totally instinctive. Maybe because I was beaten at school for every sentences beginning with “il est”, until I found an alternative without really understanding why.

Now about your question regarding the position of the adjective, a few a fairly predictable: for example color follows the name (la voiture rouge), petit and grand are always before (un grand appartement but un appartement spacieux, un petit homme (small) but un homme petit (mean)). In facts, the adjective position is a research subject in french theoretical linguisitc.

The best way to know which substantive a adjective refers to is the gender. Yes, there is a reason why in french gender is not related to the sex. With the gender and plural agreement, and the facts that the adjective is never very far from the name, you have really very few chances to misinterpret the reference.