How difficult was it to design Chess? Was there multiple, evolving versions of it? How did it spread across the globe like it has?

Chess was most likely created in modern-day India roughly 1500 years ago, where it was called "four members" (chaturanga), referring to the 4 parts of an army: cavalry, elephants, chariots, and infantry. The earliest rule sets are lost to time, but it looked similar to modern chess. It was played on an 8 by 8 board with a row of 8 infantry (pawns) and a row of more powerful pieces: 2 chariots (rooks), 2 horsemen (knights), 2 elephants (bishops), the king, and the king's adviser (queen). The elephants probably moved exactly 2 spaces diagonally, without jumping, the adviser probably moved exactly 1 space in any direction, there was no en puissant move for the infantry, and it's not clear whether the horsemen could jump over other pieces.

Clearly this was meant to simulate militaries of the time, with an emphasis on the importance of chariots. The elephants/bishops and adviser/queen were much less powerful in early versions of the game, thus placing a much greater importance on the chariots/rooks, which could move quickly across the battlefield, and served as mobile archery platforms for elite bowmen.

From there it spread west to become the Persian game shatranj, and probably spread east to become the Chinese game xiangqi ("elephant game"), also called Chinese chess. However, some Chinese sources claim that xiangqi was invented independently. Xiangqi is played on a 9 by 9 grid with 5 infantry spaced out, 2 cannons that must jump over other pieces to attack, and a back row of 2 chariots, 2 horsemen, 2 elephants, 2 guards/advisers, and the general, which serves the same role as the king.

https://en.wikipedia.org/wiki/Xiangqi#/media/File:Xiangqi_Board.svg

According to legend, the general was originally called "king" or "emperor", but one day the Chinese emperor overheard two people playing the game, and one exclaimed, "I killed your emperor!" And that's when the piece was renamed to "general."

But xiangqi is quite similar to chaturanga, in particular with the elephants moving exactly 2 spaces diagonally. Although in xiangqi they're not allowed to cross the center row (the "river"). Xiangqi spread to Korea to become janggi, and to Japan to become shogi, both of which have somewhat different rules from xiangqi.

To the west, the game spread throughout the Muslim world, and "chaturanga" became "shatranj" became "shah", which eventually became "chess". This is when the pieces became abstracted rather than statuettes, due to the Muslim ban on idolatry and iconography. The game was introduced to Europe through Spain with the Umayyad conquest of the Iberian peninsula, but it also spread northward into modern-day Russia.

But it's in Spain that Chess began to change into its modern version. This is where the adviser/vizier transformed into the queen, the elephants transformed into bishops, and the chariots (Persian "rukh") became towers (Italian "rocca"). Especially, the reign of Isabella -- combined with a desire to speed the game up -- led to the creation of the modern rules for the chess queen, where the queen is the most powerful piece. This was also where the bishops became more powerful, and castling and en puissant were introduced.

The modern rule set was formalized in Europe by the 19th century, but I also want to mention an Ethiopian variant of the game -- senterej. This is quite similar to modern chess, but during the opening phase, players may set up their pieces within the first 4 ranks however they like, without regard to how many moves are made. They're just not allowed to cross the center line of the board.

For sources and further reading, I highly recommend:

Birth of the Chess Queen, 2004, by Marilyn Yalom

Chinese Chess, 1985, H.T. Lau

Chariot, 2005, Arthur Cotterell