1.89 in. x 50 yd. 322 Multi-Purpose HVAC Foil Tape

No, this tape is just a thin metallic tape.

Yes it sticks well.

Yes it would work well

It is for use outside of the dryer, it is for connecting the joints of pipes, I would not recommend it for any other use.

This product was really good. I purchased it to seal up the thermal blanket I purchased for my water heater. Only if our president did this good of a job.

It is water resistant to a point, it will not seal joints under water.

I have used this extensively, and never had any smell in the house even immediately after use. The adhesive side of the tape should contact the outside of the pipe only, it should not come in direct contact with main air flow. According to the manufacture the joint should be made up solid with little to no gaps in the metal pieces. The tape is applied to the two surfaces to stop transient air flow where the joint does not seal. That puts the tape out side of the flow going to the living space.

It is a product that works well and I will buy it again !

Yes, just make sure the fixture is rated as enclosed can or you might need to change them out. If you do this make sure to use LED bulbs as lower heat to prevent overheating and fire.

Possibly, but not well, and not for a long time. This tape is designed to be used indoors to seal the joints in duct work (and it does very well, at that). It is not intended to be exposed to the elements, and if it's applied to wood (which it doesn't do well), it will tend to trap moisture, and perhaps accelerate disintegration. If you wish, you might try lining the tops of the rafters with strips of self-adhesive rubber membrane (often called "Grace" in the roofing industry, HD SKU 204423144). This material would tend to be much more resilient for this application. It only comes in large rolls, so you might talk to a roofer to see if s/he has remnants of Grace available from a local job. That would help divert those remnants from the landfill. Good luck.