I have used a T-Cell a lot and love it. It's one of the few gizmos to hit the market that actually works as advertised.
To try to answer your questions:
1. Yes. Now I wouldn't hold my face over the appliance and huff that stuff, but you're not going to poison yourself or asphyxiate in a ground blind.
2. Probably. But it's a naturally occurring substance and I've not noticed any deer spooking when I used it. But if a deer can smell the T-Cell, they can smell you, which is likely the bigger problem.
3. All I know is I stop getting bit and/or harassed by bugs when I use it. Even if it doesn't directly affect biting gnats or other insects, its performance on mosquitos alone makes it worth its weight in gold.https://wildernessinstinct.com/is-thermacell-safe-to-breathe/
The EPA has approved of both allethrin and the Thermacell device itself as a safe and effective means of repelling mosquitoes with minimal effects on the environment. Unless you are someone with extreme sensitivity, or a cat, use of the Thermacell device should pose few problems. As well, if you are in an area with lots of mosquitoes, the minimal problems that may be posed by allethrin exposure due to the use of the Thermacell device are likely going to be much less pertinent an issue than exposure to the West Nile virus.