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