Electronic – Mic amplifier noise

The resistor is needed so that your bypass capacitors have an R with which to form an RC filter. The 22 uF and 0.1 uF capacitors do not effectively remove voltage noise from the 2.2 kOhm resistor because they are in parallel with it.

But when the 100 ohm is added, then there is suddenly a voltage divider, the bottom leg of which is bypassed by the capacitors, for alternating currents.

Your circuit:

^{simulate this circuit – Schematic created using CircuitLab}

DC equivalent: 100 ohms doesn't do much next to the 2.2 kOhm:

^{simulate this circuit}

AC equivalent:

^{simulate this circuit}

Here is the AC equivalent circuit if we don't have that 100 ohm resistor there. Now that node is not exactly at AC ground but caught between two impedances: those of the capacitors and the inductance/resistance of the wire. Any noise flowing through there now has more of a chance to enter the 2.2 kOhm resistor and thus end up amplified.

^{simulate this circuit}

Your question is too long to read, so I'm only responding to the schematic. It's not clear which schematic you are asking about, so I grabbed the first one. To keep this answer consistent if the question is edited, here is the schematic:

1. 12 V is quite high for driving a electret microphone. 3-5 V is more normal. Check the datasheet.
2. 22 kΩ is quite high for driving a electret microphone. Did you even look at the datasheet?
3. Noise on the supply will be directly coupled onto the input via R3.
4. C4 and R5 form a high pass filter at 1.6 kHz that affects the overall frequency response of the amp. Frequencies below 1.6 kHz will have less gain. This makes no sense. Rolling off gain below 20 Hz is fine and is still considered "HiFi" audio. Rolling off at 100 Hz or so can be acceptable in some cases. Rolling of at 1.6 kHz is just bad.
5. You are asking for way too much gain from a single stage. The gain you are trying to achieve (above the 1.6 kHz high pass) is (R4+R5)/R5 = 2.2k, which is absurd for a single stage. Let's say you only care about frequencies up to 10 kHz (HiFi goes to twice that), and you want 10x gain headroom for the feedback to work well. You are expecting the gain bandwidth product of the opamp to be 2,200*(10 kHz)*10 = 220 MHz. Even without the factor of 10 for the feedback that's way out of line.
6. R6 makes non sense at all. I can't even guess what you think it does, but what it actually does is waste 1/2 the gain.
7. The volume control on the output isn't a good idea, especially when you are expecting such a very large gain. Loud signals will clip before you can attenuate them with the volume control.

To fix points 1-3, use a resistor divider to make the right voltage for the electret. 20 kΩ on top and 10 kΩ at bottom will divide the supply by 3 to make 4 V, which is probably in the intended range of the electret. To filter out supply noise, break the top 20 kΩ resistor into two 10 kΩ resistors and put a cap to ground between them. The divider impedance at the cap is 10 kΩ//20 kΩ = 6.7 kΩ. That requires at least 1.2 µF for the rolloff frequency to be 20 Hz or less. You seem to have a bunch of 10 µF caps around, which would work well.

Connect the + side of the electret to the junction of the bottom two resistors. This drives the electret with 4 V at a dynamic impedance of 5 kΩ, which is a lot better than the existing circuit.

To fix the gain, it's good to start with what the opamp can do. The TL071 has a typical gain*bandwidth of 3 MHz. Let's say we want a gain of 10 headroom for the feedback to work well, so that leaves 300 kHz. Assuming HiFi audio, the gain should be flat to 20 kHz. That leaves a gain of (300 kHz)/(20 kHz) = 15. This was based on the typical, not minimum guaranteed gain. However, the factor of 10 for the feedback isn't exact. If it's only 5 at 20 kHz the closed loop gain will still be reasonably flat, so lets aim for 15x voltage gain.

15x voltage gain means R4/R5 = 14. Keeping the existing R4 means R5 should be 1.57 kΩ, so 1.6 kΩ it is. The C4-R5 filter should roll off at 20 Hz or lower, which means C4 must be 5 µF or more. Keep the 10 µF.

With a sane gain, you need extra stages to get line level and beyond. One advantage of this is that you can leave the volume control where it is, immediately after the first stage. The signals in the first stage won't be large enough to cause problems, even when very loud. 10 mV from a microphone would be a lot, which times 15 is only 150 mV, so that's all fine.

Or work it backwards. The TL071 might be able to swing 8 Vpp in this setup. That divided by 15 means it won't clip as long as the input is 500 mVpp. No electret or dynamic mic is going to put out that much.