About tip 1 what kind of buffer and how should I wire that?
I don't think that particular module/chip has differential audio out, its single ended, with both left and right channels sharing a common ground - AGND. Modules like the CSR8645/8670 have L+,L-,R+,R- with built in drivers meaning they can be connected directly to the drivers in headphones, but require a differential to single ended circuit if they are to be used for systems with a common ground (like headphone jacks). Your module is more convenient, as it doesn't require conversion, but this also means noise will be higher as there is no way to cancel it out.
2 the AMP uses 5V from a SMPS and BT module 3.3V from a linear voltage regulator but still sharing the same ground but I don't think that matters.
Thats good, sounds like their power supplies have enough filtering between them. But when you saying 'sharing same ground', is this just AGND? or the ground of the power supplies? or both? The reason I suggested separate power supplies is because with one power supply derived from the other, you still have a common ground. This is
as well as the AGND for the audio. This means you have two grounds, one for power, and one for audio. I was suggesting you try and use two separate power supplies, with two batteries, just for testing, to see if that cures it. If you can only have one power supply, you can get isolated power supply converters for this purpose. This effectively eliminates the common (power) ground between BT module and amp.
4 that'd be annoying I want it to be professional yet the design has to be simple quite small and thin.
I believe the manufacturers of BT dongles have already done the best they can. Some are noisy, because they were designed and manufactured to a price point - you can't expect to pay $5 for one and get crystal clear sound. But getting towards $20-$30 and there are some that are pretty damn quiet. Avantree is a popular brand.
As an alternative, which may open up a can of worms (ie: they are a bit of a sod to work with) the CSR chipsets can be remarkably good for audio, given they use the built-in Apt-X codec. The higher quality is only really noticeable with headphones, and they can still suffer the problems off crosstalk, noise, beeps etc..
Found a link, this guy also recommends isolating power supplies!
http://www.penguin.cz/~utx/hardware/Bluetooth_receiver_Enjoy_BT-AU01/#hack_to_silence_idle_noiseGood luck.