Istikhara and marriage

Istikhara is not strictly for marriage. It's for asking Allah for guidance towards the thing that will be best for strengthening piety and faith, for the ultimate success in this world and hereafter. For example, if you can't decide between two jobs, you can pray istikhara for Allah to guide you to which is best for you. If you want to travel somewhere but are unsure whether you should, you can pray istikhara. You can only pray for something which is halal not sinful. You also have to realize what is best for you doesn't mean what you think is best for you. You're putting all of your trust in the Almighty and asking to be guided to what Allah knows is best for you. That doesn't mean you will be free of trials after the choice is made, because our journeys are always ongoing, but that you have trusted in Allah to guide you towards this thing which in the end will have been good for you and a reason for success. I hope I'm making some sense.

This is the du'a/supplication (which is done after prayers):

(O Allah, I seek Your help in finding out the best course of action (in this matter) by invoking Your knowledge; I ask You to empower me, and I beseech Your favor. You alone have the absolute power, while I have no power. You alone know it all, while I do not. You are the One Who knows the hidden mysteries. O Allah, if You know this thing (I am embarking on) [here mention your case] is good for me in my religion, worldly life, and my ultimate destiny, then facilitate it for me, and then bless me in my action. If, on the other hand, You know this thing is detrimental for me in my religion, worldly life, and ultimate destiny, turn it away from me, and turn me away from it, and decree what is good for me, wherever it may be, and make me content with it.)

format_quote Originally Posted by Artic090

1) If I am not a Muslim and dont now the prayers, can a person (obviously a strongly practicing Muslim) do Istikhara for me?

Each person does istikhara for himself.

format_quote Originally Posted by Artic090

2) Usually, what are the signs / dreams that indicate the negative or positive outcome? Do you know some examples of dreams...?

Some people may have dreams, but dreams aren't always indicative of outcome. It's more about the circumstances surrounding you and strong feelings towards this choice. For example, say you were going to marry a girl and you thought she'd be good for you, and so you prayed istikhara before asking for her hand. Afterwards, you may start feeling a bit doubtful about her even though there's nothing about her that you thought was really wrong. You just start having a feeling that maybe there's some incompatibility or it's just not 100% as perfect as you'd want it to be. Later on, you plan to meet her family anyway, but while you are trying to make the plans they keep getting changed or something comes up that prevents you from doing so. Basically the road towards actually attaining this marriage becomes difficult or doubtful. This would mean that this marriage is probably not for you. Alternatively, if everything goes smoothly and you feel really good about the marriage, and you see only good things happening around you, then this is a positive result of the istikhara and you should go ahead with the marriage.

format_quote Originally Posted by Artic090

3) Hypothesis of life: I'm going to marry a girl. I know her, I like her, I think she is perfect for me. But I want to make sure that my God gives the certainty that this is really the woman of my life.
And in fact God, through a dream, gives me the signal that I can marry her.
But this happens! That my wife will ruin our marriage with some wrong attitudes.
In this case, why Istikhara did not work? Why did God give me the "green light" to marry that person who turned out to be wrong?

Life does not end at marriage. Marriage is just a part of life. Through a failed marriage a person can become a better person, a better father, a better believer, etc. It can be a preparation for something bigger and better for him. It all depends. Also there's a lot of hadith and verses in quran on how to choose a spouse, how to be a good spouse, and about marriage in general to help guide believers so that they may maintain and have successful marriage even through difficult times. Trying to fix a marriage is better than divorce. Divorce is a last resort, and even then it should not be vile or unjust. Marrying someone should be taken seriously and not simply be based on vanity purposes.

format_quote Originally Posted by Artic090

4) Are there other similar prayers like Istikhara?

Du'as/SUpplications are considered changers of destiny. So absolutely! Any sincere du'as and prayers made are accounted for. There are also many specific du'as that come from the quran and sunnah. There is a proper way to make du'a which I won't go into, but if it's something you're interested in reading about you can read this book (pdf).

You can read about istikhara here Istikharah Prayer - (asking Allaah subhaanahu wa ta'aala for guidance.) This is a very good guide that explains it in much better detail than I have.

I hope this helps