Some things just dont make sense to us humans. There are many things we cannot understand about this world. We need to be able to have free-will to choose the creator over His creations. I really have a hard time doing it though and it makes me depressed. I get on these spiritual "highs" where I am ready to die al kiddush HaShem and then I get on these spiritual "lows" where I want a refund for all the time I invested in Judaism. How do I strengthen my emunah? I am willing to do anything. Right now I feel like I am just frum because it gives me a sense of purpose and it is helpful for my mental health. Those are both selfish reasons. I feel like it would be better if I werent frum then if I were frum but had this selfish mindset where it is all for me and out of love for me and not love for God.Finally I am just wondering how a Jew having faith or "emunah" is any different than a muslim ignoring the contradictions in the quran and believing Islam is true based off of "faith"?  

Ups and downs, or "challenges" are an essential part of life. If everything was always "up" and easy, we wouldn't have any pleasure when succeeding, for it would just be automatic, and we wouldn't have the pleasure of free-will. Emunah is no exception. Nevertheless, you seem to focusing on the emotional aspect of feeling close to God and Torah, and emotions, by definition, have "ups and downs". On the other hand, the intellectual side of Emuna is more constant and eternal, less prone to the dynamics of life. Find a good chevruta (study-partner) with whom you have "chemistry" in the dynamics of learning, and choose a good book which speaks to you. In recent generations, Rav Soloveichik and Rav Kook seem to be the most successful and obvious choices. Similarly, find a rav on the internet who inspires you, and make his classes a regular part of your schedule. Take advantage of the internet which offers endless types of classes, on endless topics, and you'll definitely find the spiritual "food" most fitting for your taste. Also, during tefilla, speak with Hashem, and ask Him to help you in this most important topic. He wants it, and you want it, so there's no reason it won't succeed (although it may take patience, like all good things in life). I admire your striving to believe and connect to Torah out of a stiving for truth, and not some selfish need. That's surely the ideal, but we are humans, and as you wrote, it would be much better if we could strengthen our motivation for Torah and Mitzvot, to observe them out of identification, love and belief. Almost anything which strengthens our belief is positive, but there are different levels. One of the keys to belief in Judaism is precisely your final point. As opposed to any other religion, Jewish history- uniqueness is probably the best way to see God, and always was. When there were prophets, even the Christians and Moslems accepted that they were mainly Jewish. God not only revealed Himself to Am Yisrael at Sinai, but also spoke to our many prophets. Today and for the past 2,500 years, He prefers not to do super-natural miracles and not speak to man in prophecy, in order to enable us a higher level of free-will, just as a parent wants his child to mature and be more independent. But today, still the easiest way to see God is through the prophecies to Israel which were given 3,000 years ago, but today are being fulfilled. To gather Israel from 103 countries from north, south, east and west, and return us for the 3rd and final time to the Land of Israel, just as He said He would (Dvarim 30, 3), has no parallel in any other nation. The eternity of the Jewish people and our disproportionate role in history and the modern world, speaks for itself.