Why did Allah(SWT) make some stuff makruh instead of halal or haram?

As a mercy for us. Some things are less preferable but not haram. If everything was haram than this would be very difficult on us.

1) Are exams permissible reasons to not fast, and then make them up later?
2) Is narcolepsy a permissible reason to not fast and pay for the poor instead?

No, exams and narcolepsy are are not valid reasons to miss fasts.

Am I allowed to open my fast as soon the adhan is called?

Yes

Are collecting pokemon cards haram? No gambling, just trading and collecting? I’m asking because they’re still cards you know? Also would it be haram to sell Pokémon cards? I have some that I want to sell

No this is not haram

How should one deal with homesickness?

Try to visit when you are able, call or video call home often. Make friends in your current location and find activities to do there which keeps you busy and builds in you a fondness for your new place.

Is dog fur najis? if me and my clothes are dry, and the wetness of the dog hasn't touched my clothes, can I pray with those clothes?

Yes Dogs are impure (najis). However, Dry upon dry does not transfer impurity (najasat).

I would like to know if someone is making the intention to do ghusl medium istihaza, will my ghusl be inorder to make the intention I am making ghusl istihaza qurbatan ilallah or I have to say I make ghusl medium istihaza qurbatan ilallah?

Your ghusl is in order either way. Intention does not need to be spoken aloud, but intention is that you are aware of what you are doing and that you are doing this action qurbatan ilallah (for seeking nearness to Allah).

If someone during ghusl forgot to wash their face, will the ghusl will be valid if the person just wash the face?

Ghusl by shower needs to be done in sequence: Head/Neck, Right side, left side.

I recently got released from prison after being wrongfully accused and convicted. By the grace of Allah my innocence was proven and I am home now after 10 years. I still question how that happened to me why Allah allowed it to happen and allowed injustice to happen to me on such a scale. I am low back in society and it is hard to readjust and sometimes I feel like I am a failure and I have not yet achieved anything in life especially when I see how my friends became and how successful they are know. Al hamdulila for everything but I still question my destiny and I don’t know how to live forward and move on. It is hard for me to open up and explain more but I pray that you are understanding my struggles and my inner battles. I strive hard to stay on the right path and do my daily practices and I thank Allah daily for freeing me and helping me but I can’t seem to understand why I had to go through all this pain and suffering and injustice and oppression.
Also society is not merciful and I keep getting questioned and looked at different by people once they hear prison even though I got proven innocent and that puts me even more down and discourages me. Please give me some insight and advice and sense of hope.

Wa alaykum salam. I understand. I myself did 9 years in maximum security. It takes a lot of perseverance to make it brother. Check out this lecture https://youtu.be/N5R3PxrUsn8

I also founded a program to send books into prisons www.2ndchancebooks.org

May Allah make it easy on you brother

I had the habbit of masterbation. I couldn't control it, and after 14 days in the month of ramazaan, I masterbated. However, I had an intention that I will masterbate but not ejaculate, and ejaculation happened eventually even though I did not had the intention to masterbate, I then watched some videos and found out that I have to carry on with my fast and do not break it. I sincerely repented afterwards, and then I did not perform the qada, now I remember about it, do I still have to perform qada or give kaffara as well. My intention was to only Masterbate but not ejaculate, however ejaculation took place, do I still need to give kaffara or just qadha?

Qadha is required but not kafarra in this case. You should turn away from this action and turn towards Allah. When we are fasting it is not only refraining from food and drink but also we fast with our eyes, ears, tongue and limbs by staying away from those things Allah would disapprove of.