I don't want to give you a fish, I'd like to see you learn how to fish instead.
The purpose of analysis is, in my opinion, to get a perspective into the music in order to somehow work with it, relate it to existing pieces, existing patterns, to create variations, orchestration, etc. Dissect, divide the music into its components, building blocks, to get a hands-on feeling of what the harmony is, what melodic possibilities there are. What is essential, what can be left out. A good basic analysis method is, in my opinion, the following:
- Find the key, the tonic, the home note, and if that's a minor or major chord. In your example case the home chord is E minor, meaning that E minor is a harmonic center point and an E minor could work as a "for dummies" ending chord. (Forget about "harmonic minor", that's a scale, not a key.) This step tells what is number one in your Roman numerals.
- Find the bare essence of the chord progression in terms of simple triads. If you had to play this on the left-hand chord buttons of an accordion, which buttons would you use. Dumb it down a bit. Or a lot. A basic go-to set of chords to try for a song that's known to be in E minor would be something like Em, G, Am, B, C, D, F#, A. (Maybe add F# diminished, if you have that as a basic chord in your chord vocabulary.) This step decides the Roman numerals for the chords. Since home, Em, is "i" (Roman numeral one, but written in lower case to denote its being a minor chord), C would be VI (Roman numeral six written in capital letters to denote it being a major chord)
- Maybe at this point you might already add some melody notes, for example add the A note as melodic note over the E minor triad in B E G A. The top notes, B B A A, seem to form a nicely lead voice. It doesn't have to be the final lead melody, but it does draw attention.
- Find the bass line - maybe there are bass inversions. In your example case, depending on how low a B you use, the B E G chord could be an inversion of an E minor, which you would write as Em/B. Though if you only played it rather high up on the keyboard, then maybe B E G is just a right-hand fingering, and you'd play a low E as the bass note instead.
- If the basic triads with bass inversions don't get you close enough to the target harmony, add more notes to the chords, for example adding a B note to a C major, C E G B is a Cmaj7 chord.
- To get a feeling of the harmony, poke around and try to get a feeling about what other notes you would use, if you had to add melodic lines or solo over the chords. For example over the C E G B chord, i.e. Cmaj7, I would NOT play a D# note, that would sound horrible. But a D natural is OK. So there goes your "E harmonic minor" idea in the trash. Good riddance. Music is not in a scale (except modal music), there are chromatic alterations. Now D is natural, now it's sharp, now it's natural again, now it's sharp again. Chromatic alterations.
What comes to your C D# F# B chord, you could see it many ways. Someone would press the C dim button on the accordion, others would try B major or maybe C minor (re-interpreting the D# note as Eb). This changes the Roman numerals. If you consider that most elemental essence of the chord to be B major, then the Roman numeral is V. But if you think it's more like Cdim, then it would be "vio". To me, in this context, the chord is an inversion of V(b9) i.e. B(b9).
As general advice, if you're playing four-note chords on the piano, and if you can't understand i.e. reason about what's happening, try to reduce it to three-note chords, preferably triads. Something that you DO know. And if you aren't familiar enough even with basic triads to get that "I know what I'm doing" feeling, then you have to play more songs by ear, finding chords by ear. Make it simpler and repeat until it's so simple and familiar that you know what you're doing. Every complicated thing builds upon simpler and more elemental things.
About your in-between chords, that seems like stuff that our accordion player wouldn't try to do at least not with the left-hand chord buttons. Nice note combinations, they are! But you'll have to get more music under your belt, to see those as an application of something simpler, IMO. Play more music by ear and get familiar with simple things.
