The point is i am unable to do it further. Whichever combination of resistors i use the gain is similar.
You need to use an op amp that will work rail-rail if using a single (5V) power supply.
The MCP6022 would be a suitable choice.
It would be good if your schematic showed power supply connections?
Your signal looks very much as if its just noise. the zener may be too low an impedance to allow the piezo to do much.
I don't know how piezos are to use, but taking them as pure floating AC-source, I would connect to the left connection/wire of the most left 10k resistor to ground to operate the OpAmp as non-inverting amplifier
1Megohm across the piezo is needed, but will also create a high-pass filter.
Not good for low-frequency heart beats.
Maybe wise to increase that to 10Megohm.
That also means you should use an opamp with fet inputs (rail2rail and for single 5volt supply).
I have connected it to ground. Virtual ground.
Ah, yes, ok!
Thank you @MarkT ! I tried your circuit idea with MCP6022 op amp as @johnerrington suggested (thanks!) but with slightly different setup - pic 1
Notice, I didn't add resistor for gain loop. Too by honest not sure why it works without them better, but the results are very satisfying - pic 2
It can now detect light taping in the other corner of the bed, sick
One thing i noticed is the noise which constantly rises and diminishes - pic 3
How can I mitigate this?
Its no surprise you are seeing noise.
Your schematic shows the cap coupling to the Vcc+ where of course it SHOULD be to ground.
Also you need to ensure that no noise is introduced on the ground line so the cap, 0V to arduino and op amp should be a star point.
The resistors IMHO could usefully be larger - say 12k not 1k2 just to reduce the current from the supply.
Also your op amp configuration is "a bit unconventional" and could be causing the op amp to oscillate.
The two R's and cap create a "mid point earth" so lets redraw your circuit to see what is wrong
You can see the output of the op amp is GROUNDED.
Put a resistor (R2 typically 10k) from the output to the inverting input. You can adjust the gain by the value of R3. With R3=R2 gain = 2; With R3 not connected gain = 1.