PWM to analog 1-10V converter: help to understand how it works
From your OP-Amp Datasheet, we know that the output can go from (VCC-)+300 mV to (VCC+)-400mV, so for this application, i would supply 12V to your OpAmp.
The exact value is not that critical, you just need to design it so the cutoff frequency is well below your PWM frequency, but not too low to avoid lowering your DAC max bandwith
Yes it should be connected. But however, this layout is very problematic, no decoupling/filtering whatsoever, i would redo the whole thing.


But if i were to be honest, my advice would be to redesign your own DAC, it is not that difficult, and you could easily achieve better results than with this thing you have here.