As you've probably discovered, there is a lot of variation. Most of these decisions should be made case by case to make sure the footnotes work as something clear:
- Numbers vs symbols vs letters vs Roman numerals: Generally speaking, numbers work when there can potentially be many footnotes or endnotes in a series. Symbols work when there are definitely only one or a few - they more clearly stand out, but are less flexible. Letters can work better than numbers if many of the things with footnotes are numbers themselves, or if the text includes superscript numbers with other meanings (e.g. mathematics and chemistry). Roman numerals are a possible last resort if for some reason nothing else works and you are confident your audience understands them. Sometimes, people use numbers for endnotes (e.g. references) and symbols, or sometimes letters, for within page footnotes with a different meaning (e.g. clarifications).
- The character in the note itself is
often full size (and pretty much always full size in endnotes). The key is, that the character in the text should stand out as something separate to the main text, to minimise disruption to reading, and it's corresponding note should stand out to someone searching the page for it. Reducing size and pushing it away from the baseline helps the character in the main text achieve it's purpose, but would hinder its partner in the note. A footnote number superscript in the note can help by making the correspondence more obvious and unambiguous; a subtle colour change in footnote character in the text and the note to something lighter than the main text can also achieve the same.
- There's no one answer to how notes should be separated. It's a question of what works in each design. Often, the text blocks' shape and white space themselves are enough, and this is desirable to minimise clutter and noise. Alternatives to lines include pale grey backgrounds, indenting, a thick vertical border on one side, a lighter text colour, a lighter text weight, tighter leading (line spacing), smaller text... Any element that indicates difference and that the block of notes is one cohesive element.
- Within the note, it's usually the character followed by a gap then the text, but again it depends on case specific requirements. The most important general consideration is, the character in the note needs enough white space and differentiation that it can be easily found by someone searching the page. There are plenty of ways of achieving this.
This covers most of what is true for all footnotes and endnotes. Beyond this, there are as many different sets of rules and conventions as there are publications with style guides. Find some publication types with similar footnote needs to yours, and look at what they do and how it works. Some publications have style guides that are publicly available, which could be a source for examples of how publication-specific conventions are defined.
One area where conventions are more rigid is in choice of symbols. These are usually: * † ‡ in that order. The last two cross-like symbols are technically called 'daggers' and 'double daggers' but those names aren't well known outside typography circles. A double asterisk ** is sometimes used instead of, or before, the dagger for the second symbol-marked note. More than two asterisks begin to really disrupt a passage of text and are worth avoiding unless you're making a joke about how many footnotes there are... Beyond these symbols, there are various old conventions but these are not widely known or recognised by readers, and are more likely to confuse than help. People occasionally combine asterisks and daggers to get extra symbols, like *†, but if you need that many symbols, you should really spare your readers the headache and just use numbers or letters.