Pivot cam

Yes, this looks like our 15-177 Pivot Shoe to me. Let me know if you have further questions. 

The 15-175 uses our Series 152 Coil Balances. I highly advise getting the exact sash weight. If it weighs exactly 19 pounds or a little more, then use four(4) S152-5 5 pound springs. Use a pair on either side of the window sash. This equals 20 pounds of support overall. Being within 1 pound of the exact sash weight works fine, but that's why it's critical to confirm the weight precisely. 

If by cam pivot you mean the metal cam within the 15-177, no I am afraid these are not sold separately. If you need pivot bars, the metal pins that connect with the pivot shoe, this system often uses our 26-226, 26-446, or 26-466, but you'd need to remove and compare to see if any of these are what you need. 

No, you don't want to do that. Stronger springs will actually make the window more difficult to operate. If the springs are too strong then the window will become harder to close, and could even drift up on its own. You want to stick with what you have.

Thanks for getting back to us. Bob's original recommendations seem to be on point; the 15-177 shoe with a Series 152 spring is definitely what you want.

If your sash is only 20.3 pounds then you can get away with using 5 pound weight options per spring. With two springs per side that adds up to 20 pounds of support which should be perfectly fine. 

I can't speak for whether or not the original installers used the wrong hardware or not but it wouldn't shock me. People can be very careless when it comes to this kind of thing. They'll put in any old part they have laying around the bed of their truck instead of doing the actual legwork to figure out what's really needed. I spend half my day cleaning up those kind of messes 10, 15 years after they're made. Nothing surprises me anymore.

As for which side to screw the coils, I don't think it matters too much. I see a ton of windows where the two springs are screwed onto the same hole in the shoe, but I see an equal number of windows where the springs are screwed to opposite sides. You should be fine just screwing them to the same side.