Thanks for asking!
First and foremost, do not fear troubling the moderators.
Keeping a small site like ours running is not a major job, and we are happy to help all users.
If you want your post deleted or a typo edited in a comment, just let us know.
A couple of points about deletions:
No deletion of content is permanent. This has the benefit that things can be undone, and past posts can be investigated if there is a need.
Different people see different things. With increasing reputation you gain increased privileges. Content with a red background is deleted in the sense that it is invisible to outsiders and low reputation users. Moderators can see all deleted stuff, including deleted comments.
It matters who deletes a post. Usually users can delete their own posts. Advanced users can vote to delete (or undelete, which requires them to see the deleted thing!) posts. And moderators can delete anything. Deletion by a moderator is considered more severe, and regular users can never undo it. (If a moderator makes a misjudgement, the recourse is bringing the matter up on meta.) Who deletes a post has an influence on who can see or (vote to) undelete it.
There are some limitations to deletion. For example, you cannot delete a question when it has an answer with a vote up. In these cases only moderators can delete. But that power is used sparingly, as it deletes contributions by other users too.
One of the main purposes of a Stack Exchange site is to produce a valuable online resource for anyone to use freely.
We get a lot of traffic from Google, and clicking "delete" indeed removes content from the view of the numerous outsiders.
That you see it in red indicates that you have a special power, not that deletion has failed.
It can be unfortunate that fellow active users see your blunders, but I think our users are civilized enough not to hold your mistakes against you when you remove the relevant post yourself.
If you want more thorough deletion, notice that you can edit deleted content when you can see it.
(There might be exceptions, but I can't think of any.)
So, you could just edit the text to say "Post redacted." after deletion; then nobody will see your post by chance.
(There are limitations to editing as well. If those are an issue, let a moderator know.)
But as no deletion is permanent, it is still possible to see the edit history of a deleted posts, but very few will want to go that far.
You seem to have two deleted questions.
Both of them were deleted by a moderator upon request, and therefore you are unable to undelete them and possibly even see them.
In conclusion, if you regret posting something, go ahead and delete it.
If there seems to be any problem with that, just let a moderator know.
Use a flag, come to chat, or ask on meta.
A final note:
If you or anyone else posts something too private by accident, there is a way for moderators to delete it more permanently.
If you realize that asking "How to translate these online banking passwords of mine into Latin?" is a bad idea for security, the sensitive information can be removed.
If you see anything like this, please contact a moderator immediately.
(I recall a time when someone posted their full passport information in a question on the travel site. That information was edited out but the edit history still had it all available for the more clever identity thieves. I contacted a local moderator and they erased that information.)