"In-universe" means that it is something valid or correct from the point of view of fictional story (or a universe of stories, e.g. Harry Potter)
This is opposite of "out of universe", aka "outside the 4th wall" - things which are true in our real world.
A good example of in-universe vs. out-of-universe information is:
Q: Why did this character on fiction ...
In response to your second question about which to use and how to tag, I think we should keep the current state of affairs.
The manga tag is mostly (173/183) applied to story-identification questions. Adding manhwa and manhua tags wouldn't make it easier to either answer or find those questions, so I think it would be counter-productive.
The user posting ...
A Song of Ice and Fire and/or Game of Thrones
Real life people
D&D - Dan Weiss & David Benioff, Producers of the HBO adaptation
GRRM - George R.R. Martin, writer and creator of the series
TQAT - The Quill and Tankard, the ASOIAF/GoT chatroom for the site
Books & Show
ASOIAF - A Song of Ice and Fire, the name given to the books series....
Two points: First, SF can't be "fiction based on the possible" because as far as we know, 99% (at least) of what people think is SF is not possible.
Second, it's not possible to neatly divide fantastic fiction into "Fantasy" and "SF" since much of it obviously is a bit of both.
So, a better way to talk about it is to say:
A story is SF to the extent that ...
The most traditional division between science fiction and fantasy (Which, admittedly can be blurred), is that for science fiction it is something that is based in reality and might be possible. Fantasy is not grounded in reality, so is not possible.
So, despite Arthur C. Clarke's 3rd law - "Any sufficiently advanced technology is indistinguishable from ...