A general help *Completely new to Arduino*

Hello everyone again,

I am sorry for the confusion my post is making. I am totally new to this and I am grateful for the the time you are spending trying to understand my none-sense so you can help me.

This might sound stupid but this is a premier show in a festival so I have a kind of an NDA agreement that doesn't allow me to reveal more than technical information at the moment. I promise if all goes well I will upload the final result!

I will try to explain one more time with a dumb drawing so maybe it gets clearer:


Just to avoid any comments. This is not a real technical drawing or an algorithm chart

There should be three standalone boards fetching a number from 3 different APIs online (A number around 5 - 8 digits). Each board should send its number to a middle board that gathers the 3 numbers and do some calculations. The middle board (number 4) should send the 3 numbers and the results of the calculations to a PC. I should be receiving the numbers in Processing and they should control certain parameters. Also, the PC will be open for the user to put some input that should as well manipulate some other parameters. The end result will be a visual element.

- Why 3 standalone?
Because there is a certain visual installation around each one like they should be placed on certain materials and there will drawings around them related to what kind of data they are fetching.

- Do I need to use an arduino?
I really don't know! My choice for this UNO + WiFi one is completely related to 2 main things: it accesses the internet, And the black color is fitting the installation.

- What am I asking for?
A tutorial, or any suggestion on how to prepare this board (or any other option) to connect to WiFi then fetch these numbers and the possible ways to send them to another board (that should do some math) then from this board to the PC.

I know, this sounds frustrating for rational programmers and engineers. I appreciate your suggestions that I can do this with less equipment. I am actually aware that I might do this with one board, I am even aware that this can be done with processing or Javascript without any boards or whatsoever. But again, this is an installation that follows a certain concept and that's just a decision to be installed this way.

Thanks!