The question "How were symbols for prosodic features different before linguistics became a science" presupposes that transcription of prosody predates linguistics as a science, which is untrue, at least at the level of granularity applicable to our knowledge of the history of linguistics. Linguistics as a science developed (thousands of years ago) partially as a means of representing prosody.
Representation and analysis are the same thing, in one understanding of "representation", e.g. in autosegmental phonology a string of H-toned vowels can be represented as one H associated to many vowels. This actually does not generally lead to a difference in transcription (the other sense of "representation"), although on Optimal Domains Theory, associations ("domains") are transcribed by br[acket]ting a substring of the word.
The usual way of transcribing syllables is with a period, though brackets are occasionally (rarely) used, and they generally look messy so people don't do that. Tone transcription usually is determined by a combination of fact and ideology. If a language has 4-6 levels and many contours, then accents are not a good choice and people tend to use numbers. If you have 2-3 levels and not a lot of contours, then accents suffice -- and sometimes a certain tone is "unmarked". This may reflect a frequency of occurrence fact, or a theoretical claim about underspecification (authors are not always transparent about that).
Length of segments is likewise represented sometimes with a lengthening sign after the segment, or by doubling the latter (so, gadda vs. gad:a). The latter often reflects a belief that a long segment is the same as two in a row.
