Email is not private. If you are sending something sensitive, a password on the document means an intercepted or misdirected message is not readable.
A password in the same email as the attachment protects nothing. Send it by text message, in a call, or through a different app.
Nobody can recover this for you. If the password is lost the document is gone, so write it down somewhere sensible before you send it.
Use something reasonably long. Short passwords on PDFs are broken quickly by software built for exactly that.
No. Nobody can, which is the point of encryption.
Yes, with the same tool, as long as you know it.
No. It is encrypted by your own browser.