a) This sentence makes it sound like someone has a medical issue and an object isn’t inside them. When talking about feelings or emotions I would say “People write about things they are thinking of” or more close to what you said, “People write about things they have going on inside them.”
b) Mind and heart should not be plural. Also, someone can “have something on their mind”, if you say someone has “something on their heart” they may get the right idea, but it doesn’t sound good. A more correct sentence may be “People write about what they have on their mind.”
c) If you’re referring to someone with a background in multiple physical sciences and it’s a specific genre of sciences then use “the physical sciences”, otherwise I would just say “someone with a background in physical science...”
d) “As for the writing prowess of someone with a background in Physical Sciences, he may have a disadvantage compared to writers who have degrees in Litterature.”
In English, you aren’t really in a disadvantage. You have a disadvantage. Prowess would be a better word than aspect. It’s a fancy word for skill. I then added compared to since you’re comparing two things.
Hope this was helpful.