re: "Are my job posts visible to visitors? I want to keep my job post hidden or best able to delete."
When you post a job, you are presented with an option that lets you indicate how much "exposure" the job will get... whether you want it visible to EVERYBODY (including people using Google), or ONLY visible to people logged into Upwork, or only visible to contractors who you send private invitations to.
So the answer to your question is:
It's up to you.
The DEFAULT setting gives your job posting the most exposure possible, and renders your job posting visible to visitors, including people who are not logged into Upwork. This includes people who are not even registered Upwork users.
If you want to "delete" your job posts, you can take your job postings down at any time, regardless of their exposure setting. Your job postings will be archived in a list that only you can see.
If you would like your job postings to be hidden, then simply use the most stringent privacy setting and then nobody will see your postings except for the contractors you personally invite to view and bid on your job.
Whether or not a job is ACCEPTED by one contractor has nothing to do with whether or not a job is CLOSED.
You CAN set a job to be closed when it is accepted, but this is not the default setting, and these are two different things, even though you can have acceptance trigger closing.
A job being accepted has no affect on whether or not it is visible.
When a job is closed, then it is NOT posted on Upwork any more.
So, in a sense, it is rendered invisible.
BUT: the job is still visible to contractors who are working on the job, or who applied to the job, or who were invited to the job. And the job may still be visible to people who find it through a Google search, particularly in the cached pages.
So, in a very practical sense, it isn't exactly "invisible" or completely inaccessible, but it is no longer published by Upwork to the job feeds and it can no longer be found by doing searches using Upwork's internal search engine.
Is it possible for a random Upwork user to see your job posting, think that it is kind of interesting, and post it on his highly-visible blog which is read by large numbers of people? And no matter what you do, there's no way you can get that person to remove the job posting from his blog?
Yes, that is completely possible, but highly unlikely.
Should you post things in public Internet websites that you want to remain secret forever?
No. That's not how the Internet works.