Ok...#1.Most times any wood will work.I used walnut,pine,basswood.3/4" thick.
#2.Yep heat gun,boil it,even put it in an oven at 250 for a few minutes but I'd use a heat gun and just for the handle.One thing...Measure your circumference of the bottom of the horn using a rubber tape.Even a string will work.Now cut out a perfect circle of wood the same measurement tapered just a bit to fit it because the horn will be smaller tapered too.Dry fit it till it almost goes in.It won't fit at first because most horn is not a perfect circle.Now set the bottom of the future horn cup in a pan of boiling water about 2" deep.It won't take long and it'll be soft.When it is push your wooden plug into your horn and the horn will take on the shape of the perfect circle plug.Let it cool.Put it in a vise if you got to but be careful.You can retry it with no harm.Boiling does'nt completely ruin horn if not too long.
#3.No treatment is necessary of the wood.The wood will swell from the liquid and seal itself.The only thing I do if I'm not going to use it is to keep a 1/4" deep mineral oil in it to keep it swelled.That is safe.
#4.You can put some kind of epoxy on the outside if you like but not necesary.After plug is cooled you drill 1/16" holes evenly around bottom edge say 6 or so maybe 1/2" deep.I usually just insert toothpicks in them and break them off.You can glue em in too but not necessary.
OK to get the handle like that is to just cut a strip with your cup then heat and bend it over and attach it to the base of your cup with a tack or something of your choice.