"ja nai" after a verb

Question

1) Is the plain "ja nai" after a verb grammatically correct?

   aru ja nai?

   wakatta ja nai?

2) Why use ja nai, why not a negative form of a verb :

   aru ja nai? --> nai?

   wakatta ja nai? --> wakaranakatta?

What's the difference?

Answer 1

あるじゃない{HLLLL} （ない{HL}）means "Look / Wow, there's (something)!".

あるじゃない{HLLLLH}？ means "By the way / You know, there's (something), right?".

あるじゃない{HLLLHL} means "It's not ある! / Shut up! Don't say ある!".

あるじゃないぃ{HLLLHLH}？ means "What? You mean, it's not ある?".

（だから）あるんじゃない{HLLLLL}（ない{HL}）means "(that's why) there's (something), no?".

あるんじゃない{HLLLLLH}？ means "I guess there's one".

あるんじゃない{HLLLLHL} means "It's not that there's one (but ...)".

あるんじゃないぃ{HLLLLHLH}？ means "(I thought there was but) you mean, it's not the case?"

Answer 2

You are misinterpreting the meaning of the phrases. The translation is:

あるじゃない？ = there is, no?
わかったじゃない？ = you understood it, right?

That is, it is a positive statement with a question whether it is true or not. You can parse it in two parts: わかった = you understood, じゃない = is not, where the first part functions as a adjective where the adjective describes a state of "you" in this case, so it is as if you are asking "is not (adjective)?"

Also, the natural way of saying a phrase like that is to add an ん after the verb. You can say without the ん but that becomes a bit "stiff"/"hard". Most likely the source where you heard this actually said: あるんじゃない？