According to the video, what is the etymological connection between dragons and snakes?

The Latin word 'draco' is used for both dragons and snakes.

In the Judeo-Christian tradition, what was the serpent in the Garden of Eden punished with?

The serpent was punished by being forced to slither on its belly.

The Mušḫuššu has a serpent's head and body, the front feet of a lion, and a poisonous scorpion's tail.

Daniel killed the dragon by feeding it cakes of boiled pitch, fat, and hair, which made it explode.

The red dragon appears on the Welsh flag and is featured in the Mabinogion, representing the defense of Welsh territory against invasion.

I can analyze the symbolism of dragons in different cultures' mythologies.

1
In Judeo-Christian tradition, the serpent in the Garden of Eden originally had legs before being punished by God.
2
In Chinese mythology, dragons are often associated with rain and storms, and rituals were developed to encourage them to bring rain during droughts.
3
In Western myths, dragons are often portrayed as monsters that heroes must slay, while in Asian myths, they are often seen as benign creatures that bring rain.