Insert commas where they belong. Provide a short reason.

2. Ever since you asked my opinion about the soccer field battle I've been mulling the situation over trying to determine a logical consequence.

A: Ever since you asked my opinion about the soccer field battle, I've been mulling the situation over trying to determine a logical consequence.
(Should there also be comma between over,trying? But not sure of reason)
R: Comma in complex sentence when dependent clause 1st

5. Your suggestion is excellent and I may regret not trying it but I'm going to try something else first.

A: Your suggestion is excellent and I may regret not trying it, but I'm going to try something else first.
(Should there also be a comma between excellent,and? But that would be a lot of commas?)
R: comma with compound sentence

6. May you live as long as you want, and never want as long as you live!

A: correct the way it is
R: comma with compound sentence (implied "You" never want...?

7. On the occasion of your 16th birthday, we send you our best wishes.

A: correct the way it is
R: comma after introductory phrase

8. As you rightly pointed out a mistake has been made on your report card.

A: As you rightly pointed out, a mistake has been made on your report card.
R: Comma in complex sentence when dependent clause 1st

9. I don't like it when you're upset with me particularly since it was my fault.

A: I don't like it when you're upset with me, particularly since it was my fault.
R: Not sure why. Seemed like there's a pause there. Maybe no comma is needed because it's a complex sentence with independent clause 1st?

12. If I can repay the kindness let me know.
A: If I can repay the kindness, let me know.
R: Comma in complex sentence when dependent clause 1st

13. Despite our last three reminders you have still been coming to school late.

A: Despite our last three reminders, you have still been coming to school late.
R: comma after introductory phrase

17. As you are no doubt aware we are sold out.

A: As you are no doubt aware, we are sold out
R: Comma in complex sentence when dependent clause 1st

20. Writing math tests are not difficult if you study for them.

A: Correct.
R: No comma in complex sentence when independent clause 1st

You are correct on all of them. Here are my comments for a few:

2. (no comma needed after "over")
5. + the comma after "excellent" -- this sentence has 3 independent clauses; therefore ... the 2 commas.
9. for clarity; otherwise, the word "particularly" could be modifying "me"

thank You

Great job on adding the commas in most of the sentences! Let's go through the remaining questions and explanations:

2. Ever since you asked my opinion about the soccer field battle, I've been mulling the situation over, trying to determine a logical consequence.
Reason for comma: The comma is needed to separate the introductory dependent clause from the main clause.

5. Your suggestion is excellent, and I may regret not trying it, but I'm going to try something else first.
Reason for comma: The comma is needed to separate the two independent clauses in a compound sentence, creating a clearer pause between thoughts.

6. May you live as long as you want and never want as long as you live!
Correct the way it is.
Reason: In this sentence, the conjunction "and" connects two related thoughts without needing a comma. The sentence flows well without the comma.

9. I don't like it when you're upset with me, particularly since it was my fault.
Reason for comma: The comma here is used to set off the introductory adverbial phrase "particularly since it was my fault." It helps clarify the structure of the sentence and guides the reader to understand the intended meaning.

13. Despite our last three reminders, you have still been coming to school late.
Reason for comma: The comma is used to separate the introductory prepositional phrase "despite our last three reminders" from the main clause.

17. As you are no doubt aware, we are sold out.
Reason for comma: The comma is needed to set off the introductory dependent clause "As you are no doubt aware" from the main clause.

I hope these explanations help clarify why the commas are necessary in these sentences. Keep up the great work!