Yes slightly larger sorry.
I've used a whisper internal filter - a little dinky sized one - worked fine. Works in low water level too. Supposed to use with the whisper filter inserts, so not as customizable as some other filters. Also quite quiet as long as the cord wasn't vibrating against the tank/lid.
You mean the plug is already GFCI or it needs to become GFCI? If it is already GFCI, you can use the outlet just fine. It is safer that way anyways. If it is not yet GFCI and you want to make it so (which is a good idea safety wise), you can buy a GFCI plugin that plugs right into the outlet. They also make power strips and extension cords with GFCI built in. Make sure to get one that is "automatic" as it will turn back on after a power outage / flicker. I made the mistake of getting one that didn't specify, and so any time the power flickered the tank stayed off until someone got home and realized it wasn't running.
Really every SW tank should be on a GFCI outlet, and it is a good idea to have any tank on it, same as any outlet in bathrooms / near sinks / etc. Safety first!