The meaning of "bad pitch" and "grab him and stuff under a mattress..." in the first episode of Rick&Morty

Hi, friends. I started watching Rick and Morty with English subtitles but English is not my first language, and I have a problem in understanding the exact meaning of some dialog;This Dialog is between Jerry and his wife about Beth Father:

Jerry: Whoa! What is this on the floor? Some kind of literature for a really nice-looking nursing home. Hey, honey, crazy idea bad pitch let's put your dad here. Let's put your dad in a nursing home.

Beth: I am not putting my father in a home! He just came back into my life, and you want to grab him and stuff him under a mattress like last month's Victoria's Secret?

Jerry: I told you I was ordering you something for Valentine's Day.

I have three questions about it.

1. Jerry Says, "Crazy idea bad pitch"; I found bad pitch refer to player's mistake in baseball, But I can't understand the reason it comes after crazy ideas. What relation is between the "crazy idea" and "bad pitch."

2. In Beth's reply, She says "grab him and stuff him under a mattress," I know the general meaning of Sentences, But I can't understand the meaning of staff hear (Because in some Translation, Translator translates staff as a noun! But I think the staff is not a noun (because she doesn't say grab him and his stuff ), So I believe stuff is a verb like a grab, and it refers to Beth's father. Am I correct? What is the meaning of staff in this sentence?

3. Finally, I am not sure about "under a mattress like last month's Victoria's Secret? ": I guess Beth refers to Something happened before that she found Victoria Secret's product under a mattress, and Jerry had an excuse about it. IS my Guess Correct?

Thanks for our help. I wish I could say my question in the correct and clear way.