On average, what is a residential General Contactors fee/percent?

A lot of factors to consider. Spec home or custom? How much of a pita is your brother? How much does the builder need work/ how good is he? Location compared to builders normal work area? Etc.

Also, if in Baton Rouge or close I gotta feel like a lot of builders are still very busy.

I believe people should do hard bids only with solid agreements with builders. Why would it be in your best interest to pay percent. So one instance, counters, you can absolutely spend $3k or $15k on counters based on the rarity of stone. But you pay the contractor 5x more for that? Crazy. Have him get 3 hard bids and if he isn't sure of finishes, have the 3 use the same allowances.

Buyer or sellers market where he is? If there is tons of business to be had the contractor is going to up his margin. Supply and demand.

ETA: I look for a 40% margin after labor and materials are paid in my business. It sounds like a lot but it isn't when you start weighing in the other costs of running a business.

for good work my experience has been around 20% (10% Margin,10% overhead). I've hired folks for far less and the job was not done well.

I work in a pretty high end market (750k and up). Most guys do a flat 75k-100k over CTB. I've heard the 10 & 10 model for lower end builds as well.