Actually, You are right about the power supply, (Previously I have a direct supply with through-hole PCB and had a lot of noise after then I added LDO and de-cap near opamp).
------------------------------------------------------------------------------------------------------------------------------------------------------------------------
About the Open-loop gain
1. The PEM guys are using The same Opamp IC - THS4631 but have much superior results than mine.
2. Even the OPA2188 at my operating freq. (300Hz to 1KHz) has an open-loop gain of around 80dB (Photo attached).
So, I do not think this is a major problem
------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Yes, maybe the coil itself since it is probably a good EMI antenna.
We need proper shielding for the PCB coil -- Any idea about it?