1. did not give; agreed
This sentence implies a sense of condition. The approval could only be given on the basis of a condition.
I would choose would not give.
Agreed, the past tense, is fine.
2. here I’m not sure if it is “were” or “was”. If I had to choose I'd probably pick "were".
The company - singular - requires a singular verb. Was. However I think were is possible as a past subjunctive, but I'm not 100% sure.
3. “Have you been waiting long?” Would “Did you wait long?” be incorrect?
Have you been waiting is correct, as from the context of the sentence it seems that the speaker found the person still in the process of waiting. Did you wait long implies completion, and a sense that the person was no longer waiting when the speaker arrived.
I think this is correct, but I'm not sure.
5. “are only sold” is probably right but what about “Our products only sell in large quantities.”?
Either is possible. I would go with the first.
6. Is “Have you been” the only correct answer? What about “Will you be there yet?” or “Are you there yet?”
The sentence implies the speaker is not yet in Peru. Will you be there yet is gramatically incorrect. Are you there yet is possible, but for it to be correct here the sentence would have to start I am coming to work in Peru.
Have you been there seems correct to me.
I am not a teacher.