"How much is this?"
If I remember correctly, この needs a noun following after it. So you can say この つくえ わ いくらですか (How much is this desk?) But not この わ... without a noun. If you don't want to specify, you need これ.
Yes, は not わ. And you are right の acts like a possessive marker in this and you can't possess a particle (は) you can only posess nouns.
The phrase "the guessing game" implies that a person does not know the answer. By choosing their answers randomly, also known as guessing, they are hoping to get the correct answer.
I hope that makes sense.
Should I say 'It's the first time I hear the word "guessing game".?
'That's the first time I've heard the term "guessing game"' would sound the best.