By replacing capacitor values with different ones in a circuit, will the circuit still work?
That circuit is crap.  Run away.  Just from the look of the schematic, it's obvious that whoever designed this didn't know what they were doing.  Some problems:

There are no junction dots anywhwere.  That's the standard, for good reason.  Not only is it aggrevating to look at by those that are used to seeing proper schematics, but it also results in ambiguity.  Is the node between R3 and D1 connected to the vertical line between C2 and IC1A or is it not?

LED1 is shown with current going up.

There is no connection to the cathode of LED1 at all!

The opamp power connections aren't shown (this is giving the designer the benefit of the doubt to assume he knows power is supposed to be connected).

What are the V+ and V- voltage levels?

What is "V"?  It only appears at left connected to R4.



Then there's the circuit itself:

This circuit does not "Measure skin R" as the comment states.  It measures the change in skin resistance over a narrow frequency range, roughly &frac12; Hz to 5 Hz.  If the subject's skin resistance changes more slowly than that, or if it starts out sweaty, then this circuit won't detect it.

Noise on V+ and V will end up in the signal.  Perhaps they are simply hoping that noise won't be in the detectable frequency range.  A little filtering would be a good idea.



Like I said, run away.

However, to answer you specific questions:

I do not have the 10nF capacitor that I am supposed to use but I do have 22 pF, 10 uF, 0.1 uF, and 100 uF capacitors.

So get some.  10 nF capacitors are readily and cheaply available from the other end of the internet.  Get a range of values if you plan to be tinkering with electronics.

You seem to be asking about C1.  That and C3 need to be close to the values shown for this circuit to work as intended.  C1 together with R8 set the low pass filter rolloff frequency.  Likewise, C3 together with R5 set the high pass filter rolloff frequency.  There are ways to use different capacitor values, but then you'd have to change resistors.  That changes the impedences and the gain, which also has to be considered.  In short, leave R5 and R8 alone, and use close to the capacitor values specified.

Also, does it matter if I use 1n4007 diodes vs the 1n4001

No, not in this case.  D1, D2, and D3 are used only to make a voltage a little above V1.  Just about any silicon diodes would work in that role.  1N4001 are probably what the author had in his junk box, LOL.  In a real design, these would be small signal diodes, like 1N4148.