Follow up: if the prizes for chemistry, medicine, and peace were not the first of their kind, why did they become so famous? For reasons are the Nobel Prizes considered the highest possible honor attainable in these areas?

There is certainly precedent for biology (and medicine), chemistry, and physics. I do not know about peace, and I can only speculate at the other parts of your question.

The various medals of the Royal Society are clear precedent, and, if you allow a bit more leeway, some of its lectures, which are awarded as prizes. The Copley medal is the most famous, comes with a monetary reward, and has been awarded since 1731. It alternates years between physical and biological sciences. The Davy Medal also comes with prize money, has been around since 1877 (predating the Nobel Prizes by 24 years, and, more importantly, Nobel's will by 18 years), and is awarded for advancements in chemistry.

The Royal Society's Croonian lecture (this year's winner receives 10,000 pounds and a medal) is one of the most prestigious life sciences awards. The Bakerian lecture is the analogue for physics, chemistry, geology, meteorology, ..."natural history or experimental philosophy", really.

In France, l'Academie des Sciences used to award the Prix Lalande for advancements in astronomy, starting in 1802 (it was rolled up in a new prize structure, so it no longer exists).

Sources:

Copley Medal: https://royalsociety.org/grants-schemes-awards/awards/copley-medal/

Davy Medal: https://royalsociety.org/grants-schemes-awards/awards/davy-medal/

Croonian Lecture: https://royalsociety.org/grants-schemes-awards/awards/croonian-lecture/

Bakerian Lecture: https://royalsociety.org/grants-schemes-awards/awards/bakerian-lecture/

Prix Lalande: https://books.google.com/books?id=biIgAQAAMAAJ&pg=PA460

If there were previous awards, what was the first (or the earliest we know of)?