The fact that you stated "I'm just trying to increase my imaan." in your question is a very precious thing and it is also something I had done a lot and continue to do when I think of Allah, Islam and Quran related topics.
I have no personal information or observation to prove that Quran we have today is what Quran was at our Prophet's time (I honestly don't think any information or "proof" you can find will satisfy you). We can't even prove 100% that a novel of Tolstoy is exactly the same as it was published just one and a half century ago. Not because it can't be proven, but we simply don't have the information and technology required for it. However I have a very important thing to stick to: I believe in everything that's said in Quran with my full heart, though I still think deeply about some verses to understand them better.
What I understand from Verse 9 of Surah 15 is that Quran is and will be protected by Allah. Once I accept and believe in that, then there remains no doubt for me whether Quran was ever changed or not.
Human psychology usually requires visual, touchable evidence, especially in belief related topics (even some prophets asked Allah to show them something to satisfy their hearts - Verse 2:260), but what is so precious about belief is that we believe without having all the evidences, proof we require. Believing in Allah won't matter at one moment, you know what that moment is? The Judgment Day, where everyone will be provided with the evidence they needed, but it will be too late to believe as it has no meaning anymore.
My answer may not be the answer you seek but I recommend that you read Quran again and again, especially the first verse I mentioned, so that some of your questions may be answered in time by Allah's own words.