TL;DR M-x org-submit-bug-report
What's the proper way to submit an Org mode bug,
Then follow the prompts.. you will end up with an email message buffer. If your emacs is set up to send emails, just send that email after adding additional information about the bug.
Else. copy the body of that email, paste it in your email client (like Gmail, Google Inbox, etc), also copy the auto-generated subject like:
Bug: My bug [9.1.3 (release_9.1.3-203-g33d554 @ /home/kmodi/usr_local/apps/6/emacs/emacs-26/share/emacs/site-lisp/org/)]
Include a MWE (minimum working example) in your bug report on how to recreate that issue in an emacs -Q session loaded with that specific Org version.
and are the bugs
collected anywhere for viewing their status?
I don't believe so.
I see the mailing list has bugs generated using org-submit-bug-report
(containing "Bug:" in the subject)
That's generated using the above method.
and other bugs that have numbers ("bug#XXXX:" in the subject).
Those are the Org related bugs sent by users using M-x report-emacs-bug. /Those/ get tracked, auto-assigned with a number and you can see those at http://lists.gnu.org/r/bug-gnu-emacs/
Is there a preferred way to submit bugs?
As a user, and frequent observer of this list, the first method is preferred and gets dealt with in a speedy manner. Because not everyone following the official emacs bug list use Org. Occassionally though, someone would be kind enough to forward Org-related bugs from that list to this list.
Where are the numbered bugs coming from?
Is there a place to view submitted bugs and their resolution status?
Not that I know of. This seems to be an unofficial place to list those, and doesn't look updated.