For more details, please see the FAQ, specifically section II.6, which addresses part of your problem. Scrivener is a rich text based editor, which means every single character can have its own font. If you are into writing ransom notes, that is handy, but otherwise the given reference will help you get things all looking one way.
When pasting, use Cmd-Opt-V, or “Paste and Match Style” from the edit menu. New documents get the default font as defined in the editor preferences. That only needs to be set up once.
See FAQ above.
Yes, this is where a different font for every character comes in. Changing fonts is a selection dependent thing. If nothing is selected, nothing changes. To change an entire document to a different font, press Cmd-A first to select all. But if you just want to get everything the same way, the above method is superior.