@Jay, Yes the electrode issue is the first confusing bit for newbies. EEG amplifiers of 1, 2 and 4 channel design almost 100% use an instrumentation amplifier at the front-end which is a difference amplifier. I.e. it has a positive polarity input and a negative polarity input. The amplifier only amplifies the DIFFERENCE between Inp+ and Inp-. Any common mode signal such as noise, 50/60Hz mains pickup, etc. is rejected.
The negative input is also called the reference input and most of the time, the reference inputs of 2, 3 or 4 channels are all connected together with jumper cables and run via single cable to ONE electrode. (Doing that however has a disadvantage in noise suppression).
You also need another electrode on your head normally called the DRL. The name DRL comes from ECG equipment and it's application where it stands for Driven Right Leg. It is not an input to the amplifier, but as the name suggests, an OUTPUT of the amp and "drives" the "body" to a DC level that falls within the dynamic range of the amplifier.
So for 1-channel you need a minimum of 3 electrodes (CH1+, CH1- and DRL).
For 2 channels you need a minimum of 4 electrodes (CH1+. CH2+, [CH1- and CH2- combined] and DRL.
Now what about many channel amplifiers? Instrumentation amplifiers are rather expensive when used in quantities of 8, 16, 24, 32 or even more. Not only that, but adding so many extra reference input connectors (Normally touch-proof medical DIN connectors) would make equipment (1) expensive, (2) physically much larger and (3) would be a nightmare to use because the user would end up having to jumper all these inputs together.
I already pointed out that if you jumper the reference inputs on a 2-channel amplifier, you will (at least theoretically) deteriorate the amplifier's capability to reject common mode noise. With a 8 or 16 or more channel amplifier that would be even more so. For all these reasons, many channel amplifiers as used for BCI and clinics, etc. are just about always monopolar or also called unipolar amplifiers. These only have one input per channel.
Emotiv is a 14 channel monopolar design. Emotiv also uses a DRL but it has another common input called CMS (common sense input) used as a overall amplifier ground reference.
I have not had the opportunity to open and inspect any other many-channel amplifiers, but the CMS/DRL arrangement I believe is normal practice when using monopolar amplifiers.
Some, or even many/most professional amplifiers can be configured as differential amplifiers. But normally, in that case, two monopolar channels are used and the data is subtracted in the digital domain. This will give a poor common mode rejection ratio, and thus not very good noise suppression.
OpenBCI uses the Texas Instrument's ADS1299 chip which has differential inputs (but I don't believe that they have true INA's implemented in silicon).
Finally, I don't think a poor performing amplifier will be able to cause NFB "damage". If the hardware is lousy, your measured signals will be more noise than actual real EEG data. If you process that noise and feed it back to your brain, the latter will not be able to lock on it. Only if you have REAL EEG data, obtained from self, you apply a protocol and close the loop, can that potentially cause negative consequences due to inappropriate selected/designed NFB protocol(s).
In the above paragraph, I refer to "self". What I mean is this: where you to feed processed (protocolled) data from a different person other than yourself, that too would be meaningless to your own brain. Your brain would simply reject that as noise. ALSO, there is a certain data latency. This is mostly due to the finite time your PC uses to process the data according to your NFB protocol. For NFB, this time should be kept as short as possible. If it would take a second or longer to process and feed back the data, that TOO would be not acceptable for your brain, and again, it would simply be seen as some noise.
I am only scratching the surface here... but yeah, that is how it is with a complicated subject matter.