I wonder what philosophy graduate students do
I know what they do if they study logic, but not any other branches of philosophy

"Why is there anything at all" is an open philosophical problem on the Wikipedia page. I don't think that's a solvable problem

That's kind of a silly problem to ask. It's not like the people who live in the nothing universe can ask why is there nothing instead of something because there is nothing and they can't exist

My philosophy is dismissing all open questions of philosophy as "that's a silly question. there is no use asking it"

New thread, I'm going to answer all the questions on the page here

"The problem of universals refers to the question of whether properties exist, and if so, what they are."

Yes. The properties are the ones you define as relevant to your purpose. Next

"Related to the problem of universals, the principle of individuation is what individuates universals."

Having different properties. Things are equal based on the properties you find relevant. This is why we have an Eq typeclass. Next

"Otherwise known as the "paradox of the heap", the question regards how one defines a "thing.""

According the properties you need. A thing is a thing when you need it to be a thing. Next

"The mind–body problem is the problem of determining the relationship between the human body and the human mind."

This is a psycho-biological problem best left to scientists. Next

"Firstly, what are the criteria for intelligence? What are the necessary components for defining consciousness? Secondly, how can an outside observer test for these criteria?"

...okay I don't have a response for this one. Maybe I've been exposed to the AI-ists too much

"The hard problem of consciousness is the question of what consciousness is and why we have consciousness as opposed to being philosophical zombies."

oh I wish I was a philosophical zombie
It's all evolution's fault

"‘The problem of demarcation’ is an expression introduced by Karl Popper to refer to ‘the problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as "metaphysical" systems on the other’."

There's no need. Next

"What are numbers, sets, groups, points, etc.?"

Conceptual tools. Doesn't matter if they're more than that. Next

"Are moral facts possible, what do they consist in, and how do we come to know them?"

The easy answer is no so my answer is: no