There are a few to do that. My favorites are TiteBond 2, PL200 and Gorilla Wood Glue.
Hot glue will not work as good on pop sticks as wood glue, which will provide much better bonding.
It is not dangerous to burn popsicle sticks if they are made from wood and are burnt in a well ventilated area. If the sticks are plastic, you should not burn them. Whether the glue is dangerous depends on what sort of glue it is.
I already have a hot glue gun (high temp) w/ glue sticks, so that would be ideal for me ... It's by far the best wood glue I've ever used.
epoxy works for wood and metal.
I only use white glue for paper or lightweight wood 'fixes'. - Heavier wood repairs need yellow carpenter's glue and possibly 'biscuit' joints. - Metals and plastics of any kind are NOT at all suitable for white glue.
No, glue sticks are a type of thermal adhesive.
Fusion Glue is the brand name of a new wood glue made by Aleene's. It's a urethane glue and they claim it's stronger than regular wood glues.
There are numerous formulas for hot glue sticks. Hot glue sticks can be formulated to bond glass, wood, plastic, metal, foam, plastic, cardboard and for basic applications check out a general purpose formula.
Pva wood glue
There are many glue sticks made especially for children that do not contain caustic materials. These glue sticks general are made from non toxic glue binders developed from certain food products.
Elmer's says the gel is a much tougher glue.
Glue sticks can be bought from most stationary shops. These type of shops are most likely to stock them. One would also be able to find glue sticks at some oft he big name convenience stores.