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- Is a nuclear Iran really a threat?

Probably not in the sense that they would actually nuke anyone. Even North Korea hasn't, and North Korea isn't a republic that has to worry about popular demand. The Iranian people are already fed up with being pariahs and have voted in the most moderate person the government would allow. The bigger trouble would be that nuclear Iran would inspire Saudi Arabia and possibly others to go nuclear in a regional arms race

- Why does iran want nuclear weapons?

Because while there's little danger of them actually using the nukes, doing so changes the bargaining position, because a nuclear-armed country, even if they don't have the strength to win wars otherwise, can do terrible damage such that you don't want to go to war with them, ensuring that Iran won't be messed with militarily outside of some total war scenario

- Are economic sanctions effective?

It seems to be the case, given the election of Hassan Rouhani on a platform of detente with the West (not a major turnaround, mind, but one who is willing to engage unlike Ahmadinejad, whereby some of the sanctions can be eased)

- Would military actions be effective?

Highly counterproductive, in my mind. While sanctioning has worked, actually striking would create a "rally around the flag" effect that would throw the more fanatical elements of the Iranian state back into power. It would be short-term gains for long-term headaches

- What other options are there for stopping Iran nuclear ambitions?

Beyond punishing them, there is an effort to effectively outmaneuver them. They claim that their program is purely for the purposes of peace, so offers have been made to have the Russians sell them fuel and build them reactors without Iran having to do any fuel enrichment.

I don't want to be "that guy", Khan, but OP is asking for a source.

oops <_>

Well, at least he can look stuff up based on what i said?

- Is a nuclear Iran really a threat?

Not really, but for some reason Israel see it as a massive threat and often lobby congress through AIPAC. I think it's got nothing to do with us though and it's in Iran's sovereignty what they do in there own country

- Why does iran want nuclear weapons?

it's in their sovereignty to have nukes if they want, and it will like help them if they negotiate with Israel. Also, countries with nukes have not fought another state with nukes yet, so it could be a position of strength for Iran since Israel already has some. 

~http://www.theguardian.com/commentisfree/2012/oct/02/iran-nukes-deterrence

- Are economic sanctions effective?

All they have done is hurt ordinary Iranians, it has done little to the government who carry on as normal. Also, all sanctions have done is prevent the west from trading with Iran. Trade still carries on between Iran, China and it's neighbours. 

~http://www.aljazeera.com/indepth/opinion/2013/05/2013515121958344336.html

- Would military actions be effective?

No, when was military intervention by the US in the past 100 years ever effective? (except ww2 obviously) 

- What other options are there for stopping Iran nuclear ambitions?

Why should we when the USA has 1000's of nukes? It's like one rule for Iran and another for the USA.

~http://www.dailymail.co.uk/debate/article-2103492/Iran-nuclear-weapons-Why-bomb.html

Sorry that i can't give you an answer for intervening on Iran or stopping them from having nuclear weapons but i just don't believe it would achieve anything, we have intervened in Iran enough as it is in the 20th century. I think you should look into a little history of Iran to help understand why Iran is at this point. There are key events like the CIA backed coup of 1953 and the 1979 revolution which help explain why they hate us.  

I could hop in on the discussion but I guess you're looking for actual scientific studies and papers as sources. I'm currently writing a paper on the EU's success in international organizations and I feel your pain! Don't give up

I have enough problems doing my own homework.

1. Factors of irrationality are not present in the Iranian case at the moment, although that could change. Sometimes domestic leaders are "forced" to go to irrational war due to the demands of the populace, but again, Iranians have demonstrated a weariness of any sort of national struggle.

2. Probably not. Northeast Asia is also a critical area for US foreign policy, and yet we did not deem North Korea's acquisition of the bomb to be an unacceptable development. It's unacceptable up until the moment it happens, at which point it is a fait accompli.

3. Iran's ability to fight proxy wars is limited only to certain terrorist groups, the main of which is Hezbollah. Iran would have to demonstrate a willingness and capability to conduct larger-scale proxy wars than they have. They are not the Soviet Union.

4. Sanctions have to work in tandem with diplomacy, and so far Rouhani has demonstrated a willingness to come to the table that was not present in Ahmadinejad, and this is due to the electoral mandate he received, due in turn to the people's dislike for the sanctions. Sanctions failed in North Korea because it is an undemocratic society that is unconcerned with the people's suffering due to the sanctions. Compromised though they may be, Iran still has competitive elections and a leadership that must be accountable.

5. I had not considered this. I suppose it depends on how the attacks are interpreted, and how popular the country's nuclear program actually is compared to how much of that is just the leadership wanting to be important on the world stage. Would the people consider anti-nuclear strikes to be egregious interference from the West or would they quietly breathe a sigh of relief?

Look at this when you've given up hope.

None of this will be relevant to you but i feel like adding a bit to some of what you said

2. What i meant by no nuclear states going to war is that they haven't used them on each other and war is more unlikely. Also when did China and Russia ever fight each other?

4. I had no idea that Syria was ever developing them but i hope you know Iraq was a lie. Someone who used to work in the CIA admitted it was all a lie but they all just went along with it at the time

~http://antiwar.com/blog/2013/03/19/the-lie-that-got-us-in-the-bush-administration-knew-there-were-no-wmds-in-iraq/