No, it is not a conjunction. It is the present participle of the verb to urge and can be a verb or a noun (gerund). The participles urging and urged do not function well as adjectives.
It depends. She keeps urging you to stay. They keep urging you to stay. Basically, if the noun doing the urging is plural, no "s", if the noun doing the urging is singular then it is keeps.
That is the correct spelling of "urging" (persuading).
The mother was urging the boy to do his homework now, and not procrastinate.
In conjunction with
It is a conjunction.
No, "wow" is not a conjunction. It's an interjection.
Yes, it is a subordinating conjunction. It connects a restrictive clause.
There is no conjunction of will not.Maybe you mean contraction.If you do then won't is the contraction
The word are is not a conjunction. It is a verb.
No, it is not a conjunction. The word be is a verb.
no better is not a conjunction
It can be a conjunction, as well as an adverb. As a subordinating conjunction, it connects restrictive dependent clauses.