Re #1, half-whatever demons...the examples you cite are actually something I see as taken from asian mythology. For example, there is a Japanese spirit called a kitsune, which will sometimes appear in human form and have one or many fox tails. People borrow from mythology a lot, so the kitsune, and other "half human" characters show up in stories because people base some aspects of their stories on mythology.
Re: #2, absurdly-large swords...this is something seen in anime, not SFF fiction, and I believe they do it because in art form it can look pretty cool. It's just an art style.
Do I use these in my stories? I do use half-human creatures, yes. I don't use extra-large swords, though, because I'm a writer, not a visual artist. It doesn't make sense in written form.
The reason I use half-human creatures is twofold...I like to explore ideas of what exactly makes us human. What human is, and what it isn't. Octavia Butler is one of my favorite authors, and many of her books dealt with part-humans, and explored what makes us human--I seem to have a very strong leaning in that direction myself. Secondly, if I have a part-human character, he or she is an ambassador between human and non-human. So I have a narrator which bridges the gap between something human and known, and something inhuman and unknown. I'm not forced to use an entirely non-human narrator and dilute their alienness so folks can understand him/her.
It also makes for interesting characterization sometimes. I have an urban fantasy where I have a faun character--he's half human, half minotaur. The way he dresses is affected by how he looks...he wears a hat all the time to hide his horns, and he's very body-shy and won't go swimming with people or disrobe in any way around them. If he was a purely human character, he'd seem eccentric or shy, but with a part-human character you can see there's a reason in his life he does this. You can also explore bi-racial themes without actually having a half [insert race here] / half [insert other race here] character, and one of the bonuses of SFF is that you can explore real world issues in this way without touching on Hot Topic Real World Issues hard enough to taint the viewpoint you're trying to give someone. (IE, people hear about the hot topic issues so often that when someone touches on it in mainstream fiction or the news, people react one way or another automatically. If you approach it very subtlely in a sideways manner in SFF fiction, you can discuss it without the reader realizing at first that it's a Hot Topic Issue. Some of these issues being racial, which touches back on the half-breed character thing.)
So yeah, I have a reason for half-human creatures.
