I don't think it's possible for TAQ to be stored with the primers, but I'm not sure. This storage wouldn't be long-term (a few days, or a week at most). Thoughts?
Yes, this is perfectly fine. Many companies sell PCR Master Mixes (granted, without primers):
If you choose to make your own, make sure it's stored at -20°C, and be sure to aliquot it so it's not going to be subjected to multiple freeze/thaw cycles. Obviously you should mix it well before aliquoting, but even after thawing I would vortex it to make sure all of the components are well-mixed. Make a 2X master mix, and adjust to a final 1X concentration in the PCR tube with your DNA sample and nuclease-free H2O.