favor

A: I wouldn't have asked for the favor if it wasn't/weren't urgent.

1. yes 2. yes (first verb)

But I think, "if it hadn't been urgent," depending on your intent. (i.e., what was the nature and time frame of the urgency?)

I think that Avangi's having a very good version, but I was myself of two minds re the sequencing of actions in:
"if it hadn't been urgent,"

I asked CJ to come up with a rule for a strange construction which he responded immediately.

Avangiwhat was the nature and time frame of the urgency

New2grammarI asked CJ to come up with a rule for a strange construction which he responded immediately.

Avangiwhat was the nature and time frame of the urgency

So, as you see it, the urgency has been dispensed with at the time of your reply? - A.

Edit. Sorry, I guess that's a bit special. Let's say, "dealt with

Avangi, are you saying that's the reason "had" must be used?

New2grammarAvangi, are you saying that's the reason "had" must be used?

I'm saying that you have choices, depending on what you wish to convey. You can look at "urgency" as being in your mind, or as being a factual circumstance. If you wish to imply that the asking and the urgency were contemporary, they should have the same tense, unless, as Marius suggest

Avangi If you wish to imply that the asking and the urgency were contemporary, they should have the same tense,

Great explanation. Thanks.

Thanks, MH and Avangi.

Given the situation you described, my impressions are as follows:
I wouldn't have asked if it hadn't been urgent. "More correct"
I wouldn't have asked if it weren't/wasn't urgent. Understandable, and often used, but "less correct"
CJ
(In any case, wouldn't asked is wrong.)