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.
A phrase of four or five unrelated words is stronger than a short mixed string and easier to type from a message. Send it by a different route from the file, for example the file by email and the password by a text message. If both travel together the password protects nothing.
Open the protected file once yourself before you send it, enter the password, and confirm it works. Keep the unprotected original, because the password cannot be recovered if it is lost. The password is only a lock on opening the document, and it does not stop someone who has opened it from printing or copying.
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.
No. It only requires the password to open the document. Once it is open, the person can print or copy it.