2: what are the specs of the strain guage (LINK Please)
3: a symmetrical whetstone bridge produces two outputs at Vcc/2. You need to cater for imbalance + or - so the output from the difference amplifier should also be at Vcc/2.
"AN Op Amp" isnt good enough. There are a few (countless) different ones.
Read this
Why would you want 12V to measure with an arduino?