Over the last couple of days I've been battling with very similar problems. Attached is the schematic I've built - it's compiled from various sources 
For me, adding the C5 and C7 capacitors was decisive in getting rid of the Arduino-induced noise. Place them as close to LM386's pin 6 as possible.
Here are some further ideas:
- Add the bypass capacitor at pin 7; Add the R1 + C4 at the output.
- Keep all components as close to the IC as possible.
- If working on a breadbord, don't overextend the supply and ground rails. People say they may act as an antenna and pick up random noise.
Re your other questions:
- Yes, the output voltage at pin 5 is biased to ~2.5V
- To get better mic sensitivity, try tweaking the value of the resistor between Vcc and Mic+ (R2). This article Powering microphones suggests using a 2K2 resistor, but 10K worked out much better for me.
P.S. Here are the exact component values I'm using: R2=10K, no VR1, C1=10uF, no C2
