No, it won't help. And harnessing is not always the best option, especially if the snake has cytotoxic venom. Also, do not look for a snake after a bite: doctors will not need this information, and you may run into another bite (this will greatly reduce your chances of survival).
In case of a snakebite, you should immediately go to the hospital. There is usually a 6-12 hour window after the bite to administer the antidote - not as much as it seems. The fact is that antivenom has a very short shelf life and is usually not stored in hospitals. Most likely, the antidote will still need to be produced and taken to the hospital before they can help you.
This should never be done. Correct comment from above. + in the oral cavity there can always be some kind of microtrauma, wounds that will contribute to the ingress of poison into the bloodstream and naturally undesirable consequences. It is necessary to apply a tourniquet near the bite site so that the poison does not spread so quickly through the bloodstream, and if possible, you can still prick the bite site with 1 cube of adrenaline (1 cube divided by 4 injections around the bite), to narrow the vessels and quickly take the victim to the hospital, for the antidote.
No. I watched the program with Bear Grylls and he said that in no case is it possible, since the poison can get on the palate and can be fatal