Standard yellow wood glue (PVA glue) is the best TYPE of wood glue. Type 1 PVA - or waterproof PVA glue - should be used when any water exposure is possible, and on some woods is stronger than standard PVA wood glue. Most important is a tight fit and clamping. The brand of glue is not as important as the type.
"objects"- Different 'objects' stick to wood with different glues. If they are porous, like wood or clay, then white glue is best. If they are hard like stones or gems then epoxy is best.
Depends on the surface you are sticking it to. I would start with a tile mastic glue.
Silicone would work.
The best type of glue for ABS is Oatey Standard Yellow cement.
Kraft glue or elmers glue
fevi quik is a type of glue also known as fevi col used for sticking purpose
There is no glue that is best on everything. Each glue has it's own specialised uses, and a glue that is excellent on something may be poor on other things.
Epoxy would be best for this.
Some type of silicone glue is best for this. E-6000 is a good choice
glue sticks: pretty much any brand
White glue or yellow carpenters glue will both work.
Epoxies are best for this kind of outdoor work.
I recommend a brand of glue called Goop. And if you use it, remember that it takes a full day to harden.