No, Monika cannot be deleted from the start.
Yes, you can delete Monika in Doki Doki plus.
If you don’t delete Monika, she will continue to be in your account and you will not be able to see or talk to her.
It depends on the topic. Sometimes it can take up to an hour, sometimes it can take a little more.
There is no definite answer as to whether or not Sayori can be brought back. Depending on the circumstances surrounding her abduction, it may be possible for her to be brought back to Japan, but it is also possible that she will remain missing and never be found.