From what I see, I can connect a maximum of 8 24LC256’s together. Is there really any reason I need to use the “bank stick” format, instead of just putting them right in the box?
Not really, you can also put them into the box.
The Sub-D socket variant has the advantage, that you can change the setup by plugging another BankStick into the socket instead of changing the Bank with a dedicated Bank Selection button or from the menu. I find this more intuitive, but you are free to use alternative methods of course.
Is it possible to save the data on from this array via MIDI… by default… as in without additional “programming”?.
Yes, via SysEx dumps (see doc/midibox64e_sysex_implementation.txt of the release package)
Also, the documentation talks about groups and banks. Just so I have this right, a group consists of 8 banks, and each bank is the data for one setup, snapshot, patch… whatever you want to call it. Each 24LC256 stores 1 group, so with the maximum stuffing, you have 64 banks (setups, patches, etc.)
No - each bank consists of multiple groups. The number of groups depends on the configured “group width” which depends on the number of rotary encoders and/or pots which are connected to your MIDIbox.
128 parameters are stored in a bank.
If 64 encoders are connected, you choose a group width of 64 in your setup_*.asm file, which means that 64 encoders can control 128 parameters splitted over 2 groups.
If 16 encoders are connected, you choose a group width of 16, which means that 16 encoders can control 128 parameters splitted over 8 groups.
If only a single encoder is connected, you choose a group width of 1, which means that all 128 parameters can be controlled with the single encoder.
Each BankStick can store 8 of such banks, and since up to 8 banksticks are supported, 64 banks are available.
The BankStick partitioning changes once you choose the “patch mode” instead of “normal mode”, but I guess that I don’t need to go too much into detail anymore 
All parameters are explained in the setup_*.asm file. Select one which basically fits your needs, modify it if required, rebuild a .hex file and upload it into the PIC
Sorry for all the confusion, previous users requested too many variants which resulted into a complicate configuration (they have been warned! ;))
Best Regards, Thorsten.