Editing text in PDFs is _really_ hard compared to other document formats because most PDFs don't really encode the "physics" of the document. I.e. there isn't a notion of a "text block with word wrapping," it's more "glyphs inserted at location X with font Y."
If the PDF hasn't been made accessible, you have to do a lot of inferencing based on the layout about how things are grouped and how they should flow if you want to be able to make meaningful edits. Not impossible (Acrobat does it), but very challenging.
It's part of the legacy of PDF as a format for presentation and print jobs, rather than typesetting.
Sejda.com does it. Though its free one is severely crippled
It's still what a PDF editor, as it says in the title, would do. With a quick Google I found one that I hadn't heard about before, and it let me edit some text and save it for free.
Yes, and alongside formatting challenges, PDFs commonly only include the glyphs from the font that are actually used in the document.
So if you had PDF with "Hello World" on it, you could feasibly change it to "Hello Hello", but wouldn't be able to change it to "Goodbye World" (as the glyphs for "G", "b", "y", and "e" are not included in the PDF)
Sure, you could do a bit of detective work to figure out which font it was from the glyphs or something and lookup and insert new glyphs into the PDF, but I can't imagine a generic PDF editor being capable of doing this for you.
Some editors get around this but just straight up switching the font(s) for the whole PDF, so they'll look different after saving.