Signing up with a password is NOT the only way. Through Google or LINE the farm is created right at the first sign-in, without a code and without a password: there the farm name is asked after signing in.
The email with the code sometimes lands in «Spam» - check that folder before asking for the code again.
The code can be sent again, but not immediately: the «Send the code again» button waits for a while, and the seconds left are written next to it.
What you typed before the code can be corrected: «Change details» returns you to the form.
One email address means one farm. If you signed up with a password and then signed in through Google or LINE with the same address, you land in your own farm, not in a new one.
Dots in the address and the part after «+» do not count: for the product it is the same address.
The message «Sign-up is currently unavailable» means that self sign-up is switched off in this environment. It is NOT about your farm and not about an administrator: accounts simply cannot be created here.
You cannot join SOMEONE ELSE'S farm by signing up. Signing up always creates a new farm; to get into an existing one, its administrator must add you.