I have read that the constructions with wish and If only require the use of simple past and conditional in the main sentence. Nevertheless the use of would after Wish and after If only is possible if you want others to do do or not to do something. The use of would suggests also irritation on the speaker's part. I don't understand if both constructions are possible or not and why.
You can also use past perfect after "wish" when you're talking about the past.
(1) I wish you had been there.
--> In true, you were not there in the past.
(2) I wish I had passed the exam.
--> I didn't pass/failed the exam.
I agree with the rest of what you said.
(1) I wish it didn't rain.
--> It rains. So you I am imagining a situation that if it didn't rain. Or I would say "I wish it weren't/wasn't raining." It is raining outside, so I am imagine if it weren't/wasn't raining now, I would go out and play. Azar calls it "a wish about the present." I like this explanation.
(2) I wish it wouldn't rain.
--> It is raining now, the same situation like the first one, but with a tiny difference that I am a bit complaining about the weather and I want it to stop. It's less imaginary and more of a complaint. Azar calls it "a wish about the future."
(3) If only my teacher wouldn't give me extra work.
--> Again, with "would", it is more like a complaint or a grumble.
(4) If only my teacher didn't give me extra work.
--> Again, I don't like my teacher because s/he gives me quarts of homework. I am imagining if s/he didn't give me that much, I would have more time going shopping.
What's the same?(5) I wish my mother gave more pocket money.
(6) I wish my mother would give me more pocket money.
Mom doesn't increase my pocket money.
What's the difference?
Actually they are very similar. Number six could be a complaint or a request. It depends on the context we have, say tones or facial expressions!
(7)I wish my mother would give me more pocket money.
-->Could be a request!
-->If it is a request, I think "could" is also possible here.
(8)I wish my mother would give me more pocket money.
-->Complaint! See red?