As a teenager... actually around your age, I struggled with lots of those things... except I'd be very angry at God. At one point I raised up my fist and said to God angrily, "Don't you care about what I'm going to do to them" ... I was on the verge of doing a great sin against some people. It would've probably messed me up.
I remember one struggle was evolution. I actually made peace with that idea by the idea that God could've made the universe through evolution. However, eventually I believed in the young earth model. I still struggled some... and Today, I'm much more certain due to arguments and evidence that I've found that counters the evolution model.
My point is I think you can be a Christian struggling about these controversial beliefs. I encourage you to search for those answers because THERE ARE ANSWERS!!! I wish I could scream it at the top of my lungs because so many teenagers seem to think there aren't good answers for a young earth model or to debunk evolution. THERE ARE ANSWERS!
For the big bang.... I'd ask anyone who believes in the big bang.... What came before the big bang??? What made the big bang possible??? Where did the mass of the big bang came from???? The scientific community doesn't have an answer. They don't know... but, often it's claimed to be absolutely true... intimidating teenagers like you and like they did me. However, I saw looked for opponents of evolution in order to see other arguments. One of the first explanations was that God could've used evolution to create. Another one was the gap theory... I don't remember the exact verse but in genesis, there's a verse that may have shown a lot of time passed by which may explain the age of the earth. Other have argued in discrediting radiometric dating to be unreliable based on testing it... and that this kind of dating method can give different different ages for the same thing. Carbon dating only goes thousands of years which doesn't exactly help evolution and as far as I've known is usually regarding as reliable. Recently, some scientists have discovered dinosaur tissue... dinosaur tissue! How could dinosaur meat exist??? Wouldn't it have decayed over millions of years? This has been one of the most serious blows to evolution as of late... Mark Armitage, one of the scientist who found dinosaur tissue was so confident in how harmful this was to evolution that he said, "The debate is over! Creationist win!"
Here's a video of Mark Amritage showing his findings
https://www.youtube.com/watch?v=p1S_CU3ecNU
Also, here's another scientists, Dr. Mary Schweitzer, also found dinosaur tissue..
https://www.youtube.com/watch?v=YwpNc3jcMqA
^^^ This punches the face of evolution... Dinosaur tissue doesn't last millions of years.
Here are some more resources that I've come across as struggled like yourself...
Bible Questions Answered
https://answersingenesis.org/
EveryStudent.com - Exploring Important Questions about Life and God
I was around your age when I found these... they helped
P.S. - I'd also recommend looking up Ravi Zacherias on youtube... he's quite an amazing philosopher on Christain beliefs as-well. Also... John Lennox is great and William Lane Craige.. PLease check all my recommendations... you'll be pleasantly surprised.
https://www.youtube.com/watch?v=ZD45uWxyF_Y
^^^ Ravi on evolution, philosophical relevant response
https://www.youtube.com/watch?v=OXnRGSNmkeE
^^^ John on evolution
Please check em out okay