I have a friend who says that God will give her all the desires of her heart. Her desire is to be married one day, and I have the same desire. I also know that God gives you all the desires of your heart, but aren't we supposed to be praying that His desires are our desires, not our own selfish ones? And also, does is say anywhere in the Bible that everyone will get married? I can't think of anywhere where we are promised to get married?
You have two questions there, as I see it. First, does God promise to give you the desire of your heart; and shouldn't we be praying that our desires are what God desires? Second, does God promise that you will be married?
The answer to the second is easiest. Nowhere in scripture is there a promise that everyone will get married. Marriage is a good and desirable thing, and most people get married. Most who remain single do so out of choice. Some may wait longer than others before finding their mate. But nowhere does God come out and promise that everyone who wants to get married will do so.
Now to your other question. Not everyone gets their heart's desire. Psalm 10:3 talks about the wicked man seeming to get his heart's desire. The point of the Psalm is that God's will triumphs over the wicked; so not everyone gets their heart's desire. On the other hand, Jesus promised, "And all things, whatsoever ye shall ask in prayer, believing, ye shall receive." (Matt 21:22)
I don't think that Jesus was saying that even if you pray for something wrong or with the wrong motive that you will get it. James says, "Ye ask, and receive not, because ye ask amiss, that ye may consume it upon your lusts." (Jas 4:3) This agrees with what you said about praying that our desires be His desires.
Paul, even though a prisoner, did not ask for prayers that he be set free, although he probably desired that. Instead, he asked for prayers that the gospel be spread in spite of his chains (Colossians 4:3; Philippians 1:19).
God promises to listen to the prayers of righteous people (1 Peter 3:12), but not of the unrighteous. That is not to say that he doesn't hear the prayers of unsaved people. He answered the prayers of Cornelius (Acts 10) and Saul (Acts 9) by sending them men who would teach them what they needed to do to be saved. But those were special circumstances; he answers prayers of people who want to come to him, although prayer alone won't bring salvation. In general, he answers the prayers of those who belong to Him, if those prayers do not go directly against His word.
Keep praying for a mate. But especially pray that it be the right mateone who will be kind and loving and help you live for God.