@NNC, please.
This is meant to demonstrate the difference between #3493577 and #3493659. The former talks about a previously specified meeting ("the meeting"), while the latter is about "a meeting". Although Russian lacks articles, sometimes we can express the idea of (in)definiteness without any extra words but rather by word order. (The common misconception that 'word order isn't really important in Russian' is thus demonstrated false. Although it is indeed quite flexible, the meaning often changes slightly depending on which words go where.)

The sentence is OK in my opinion. You could also use "there's" for "there is".

This meeting with the indefinite article is a meeting that has already been arranged. The speaker is asking to be reminded of a meeting organised for Monday. "Remind me about the meeting on Monday." means almost the same.

Hmm. The difference between the Russian two sentences is that the other one is talking of the meeting which has been mentioned previously in the conversation (definite in the context), while this one talks about a pre-arranged meeting as well but it hasn't been mentioned in the immediate conversation (indefinite in the context), and it would seem to me tthat his English sentence corresponds well to the latter?

>this one talks about a pre-arranged meeting as well but it hasn't been mentioned in the immediate conversation (indefinite in the context)..

Yes, I think your interpretation of the English meaning is correct.