On a single save file- during a single playthrough on a single character- all Tesseract Wells on all floors are connected- successfully accessing a Well will allow you access to all items stored in all Wells on that save file- like an external bank of items for that character. These Wells are NOT connected to the Pocket Tesseract item.
Repairing a Well requires an Electronics skill check.
Each Well can be accessed 3 times at max before becoming inactive. Each Well requires a skill check every time you want to access that single Well. Access requires a Decipher skill check to succeed. Failed checks can result in that Well becoming inactive, or in a single item within the Tesseract Well storage being destroyed.
All items in the Wells will be deleted when that character dies on that save file.
see the Devices page for more info on Tesseract Wells.