1: Some people are sensitive to stabilizers. Have you drank a storebought wine that made you sick or break out into cold sweats and hives? If not, you aren't sensitive to sulfites, don't worry about the off-flavors.
2: If you add those stabilizers to stop the fermentation at 1.01, then you won't be able to bottle carb because the yeast have been stabilized.
3: Stabilizers don't necessarily stop fermentation, but will prevent a restart of fermentation.
4: Cold Crashing stops fermentation. If you cold crash and add stabilizers, you can be 99.9% sure it won't restart.
5: Read the sticky on bottle pasteurization. I personally recommend doing it for twice as long as recommended in the sticky.
6: Honey and Cider is basically a Cyser. The ph will be very acidic for the yeast and you can expect some off flavors and aromas and at least 6 months of aging.