Not the best idea. Hardwood floor should be angle nailed down, but obviously you cant do that. I think hardwood flooring would dry out and separate in places if glued.
I have done this and I always have the hardwood installed first. Then I install the ceramic tile. To protect the hardwood floor from getting grout or glue on it I cover the hardwood floor with a soft cover (to prevent scratches) and tape it down. Then place a plastic cover over the hardwood. Then I can install the ceramic tile at the edge of the hardwood creating hardly or no seem and level with the hardwood. When its done it looks beautiful.I would install the tile first , that way you don't risk getting glue or grout on your hardwood.
Yes, it must be a glue down wood or a floating wood floor.
Definitely not, it should be angle nailed.
You can glue the tile down, only concern is there enough room for the door to clear the tile?
Nail it.
Yes you can. A number of flooring gluesare suitable for this.
yes
Scrape as much as you can with a metal spatula then use Goof Off to get the rest. It will NOT harm hardwood floors.
Rub it with Goof Off and it will soften enough to be removed.
Yes, you do. Which glue depends on the substrate.
If it has a timber floor under and vinyl is solid to the floor and not to thick screw down 10 mm ply at 150mm centres. seal ply with pva sealer prior too tilling. If it is a concrete floor it is best to lift vinyl.
Scrape off carefully with a very sharp craft knife with blade held almost parallel to the floor.