> A 'character' meaning what? […] it's ambiguity in the concept of "character"
All of this already standardised in detail in Unicode. There is no ambiguity. Read it some time to mend your ignorance, it answers all your questions with justification, I am willing to spend time on the answers only.
> the second character of sœur (o or the ligature?)
the letter œ, both character (C) and grapheme cluster (GC)
the letter o does not exist in this text (again, according to the standard)
> the second character of حبيبي (the canonical form ب or the contextual form ﺒ ?)
the letter ب, both C and GC
the letter ﺒ is a presentation form and does not exist in this text
> the third character of есть (Cyrillic t with or without soft sign
the letter т, both C and GC
the letter ь, both C and GC, is the 4th in the text
> the first character of 실례합니다 (Korean phoneme or syllabic grapheme?)
the letter 실, both C and GC
the text does not contain the jamo ᄉ
Unicode is not concerned with phonemes, only with writing
> the first character of ﷺ
is entirely itself, the letter ﷺ, both C and GC
> or ﷽ ?
is entirely itself, the symbol ﷽, both C and GC