How can I start the numbering of footnotes with 1 on each page? Is there a way to use the traditional footnote markers (stars, daggers, vertical bars, section signs, paragraph signs, etc. automatically)

You can reset the footnote counter on each page by doing this:

@page {
    counter-reset: footnote
}

You can use symbolic footnote markers by doing this:

.displayfootnote::footnote-call, .displayfootnote::footnote-marker {
    content: counter(footnote, symbols('*', '\2020', '|', '\A7', '\B6'))
}

Where .displayfootnote is to select the element with a class of displayfootnote that you are treating as a footnote (a shorter class name like footnote or fn might be more convenient) and the symbols counter style can be used to specify the list of symbols that you want to use (U+2020 is dagger, U+A7 is section sign and U+B6 is pilcrow). Footnotes further than this will just use numbers, unless you specify "repeat" instead of "symbols", then the symbols will be repeated, eg. two stars, then two daggers, etc.