Tenses

My try: 

Uses of phrase "found out":
 (the city is going to raise taxes and the action of raising taxes hasn't iniitated.)
 1) I found out that the city is going to/will/is planning to raise taxes.
I don't see much difference with this:
I found out that the city would will raise taxes.   The choice of tenses here depends on the meaning you want to give us. If you mean that there is a more planning in this situation, "going to or planning to " can be used. But I prefer "will" with find out because "will" means something more immeadiate or something decided or learned at the time of speaking.

(It's news that my friend is going to get married and he hasn't married.)
2) I found out my friend is going to/will/is planning to get married. 
I don't see much difference with this:
I found out my friend would will get married.  Hmm, here you know that he is going to get married. You have an initial informationa bout this so planning to or going to will be more proper.

Use of word "said":
3) My friend said that the city will/ is going to raise taxes.
I  see a difference with this and the sentence  below seems to be OKbut not as good as the above sentence Why? Is that because raising taxes is still in a planning stage and has not been instituted?
My friend said that the city would raise taxes. I would say that this sentence is wrong. "said that, found out that" is a past tense in form but their meanings is relarted with present events so you shouldn't use a past tense if you are talking about a present event. The difference between will and going to is simply can be explanied as I told you before. If you want a detailed information, search them in the search box above. You will find threads discussing it. 
4) My friend said the city will/is going to raise taxes after July 7th.
My friend said that the city would be raising taxes after the date of July 7th.??  -- how would you rewrite this with shifting-back the tense when a future date is involved.  

Hmm, it is simple. Changing the tenses will help you.  My friend said that the city was going to/would raise taxes after July 7th. (Reported speech) You report the news to your friend so there is nothing wrong with tense change.

Oh I think there is a problem with making our points clear. I thought you are asking us how to make a choice between "will" and "going to" in your first examples because you didn't mention about backshifting. I just thought that you are asking reported speech only for 4.