Well be very careful when 'referencing' themes or melodies or what not. When it comes to such things in music, there is no fine line, because even the intentions of the composer can't come across purely. What you may treat as a reference or parody or homage or what not can always come across as something different to the ears of the listener, such as sounding uninspired, or thinking of it as a 'rip off'. Because of that, you want to be careful and be very intentional about what you want to reference and how you do it. If you're not careful, especially if you're referencing songs you like, your ear will subconsciously want to bend the progression of the song into something near the original. It's been awhile seen I've listened to Sanae's theme, but in this case, the similarity obviously begins from the very beginning with that distinctive solo-percussion line beat. Then you start on the same harmony (or an equivalent one, again, it's been awhile) and then walk through the same harmonies as Sanae's in the same harmonic rhythm. Then you start the melody at 0:14 on the same chord tone of the harmony and even keep that same initial melodic rhythm and even the same contour for the first couple notes. At 0:34 you change the harmony, just like the original, and again create a new melody starting on the same chord tone as the original and using very similar contours and melodic rhythms for the first couple notes. You even kept that quick piano fluttering thing right before it, that transition part. The only thing 'original' is the main theme. Which, if as you say the rest were but references, works fine since the main theme should at least be different and original. And, unfortunately, and I mean no offense, it comes across altogether as just an improvisation over the bass line of Sanae's theme. I'm sure you don't want to give off that impression, so I would suggest avoiding references, making musical references are tricky business. Also don't be so attached to a particular song in mind when writing your own stuff, though this is something I too am guilty of. "I like this song so I want to make something just like it!" is a totally understanding feeling, I feel inspired to write stuff whenever I listen to things I like too, but what you want to imitate or learn from the song in question is the 'how's and not so much the 'what's. Asking yourself why you like a song, what you like about it, will enable you to find the answers and the devices in the song that make you feel how feel. Then use those devices in your own personal, creative way to create the effect you want to create.
So same with Eternal Lily River. Now that you mention that she likes vampires, it makes a bit more sense to add in a reference to the theme of a vampire. Now, is it needed? It's a cute detail, and you handle it better since later in the song you arrange it into a completely different character and create an entirely new theme out of it. And again, you need to be very careful, clever, and intentional about it. It also brings in some other questions, has she met Remilia? Music is indeed a powerful tool and part of character building, so that you would use it to support her character -- that she's obsessed with vampires -- is great. It makes me, personally, slightly uncomfortable in the beginning though, which may in part be due to what you've done with Mio's theme like I've mentioned above. I have to trust you to know what you're doing, and what you're doing that you're doing it with intention. It's all context, complex ain't it? peoples' feelings.
So, I need to try more hard to keep an atmosphere or mood through a song, ne? I'll try!
I would say this is your strong point, not your weak point. It's only a single aspect of music making, right? Some have more and some have less. I really liked that kanji character one, for example, that one had great atmosphere and mood. There's always many many things to have to work hard on.
Also I googled 'Double Flying Rainbow Scroll' and found a sheet music for what I'm assuming is just a piano rendition of the original, which you mentioned was also a piano solo piece. If this is anything like the original, and you referenced this or something like this, I can see why you had some trouble with the harmony. I guess you could say it's a 'beast', rather wild and goes off in unexpected directions and uses sudden dissonances, and I mean this not all necessarily in a good way, though the theme itself is pleasant. Your best friend is always your ear, always trust your ear first and foremost, even if the song or the sheet music might be saying otherwise. Harmony should always support the melody. And this doesn't mean that everything always has to be consonant, because you can support melodies with dissonant, tense harmonies -- in fact this is where most of the interesting parts of any piece come from-- it's just that connection must always be there.
Well if you're bored you could make me something if you'd like. You can make whatever you like, but if you want a request, then how about Alice's extra stage theme from Mystic Square, Alice in Wonderland?