I leave the WB in place for a week each year. I probably wouldn't drive cross-country like that, or cold-start it 30 times, but because it's usually only for something like 25 miles or so over 3 or 4 trips, it's been no big deal.
Also yes to the second question, the stock one is installed after the cat. Basic question: does Hydra still use the stock O2 sensor? If not (and assuming that one is heated too), then the same issue would exist wth the stock sensor!
Your answer is confusing. There are TWO stock sensors. One before the cat, one after. Yes, the Hydra can indeed use the stock sensor before the cat, for AFR control wherever the map calls for stoich (14.7:1). It does not use the rear one; some people pull it out to keep it from dying, but mine is still the original one from the factory.
Note that you can choose to use the wideband for stoich instead of the narrowband, but it probably doesn't react as quickly as the narrowband. Regardless, it's helpful to leave the front narrowband in as a sanity check on what the wideband is doing, to say nothing of making a changeover to stock easier.