Forbidden permission and editor error after update to WordPress 5.1.1

Enable DEBUG in wp-config.php
OR
Check the Apache and / or NGINX logs for a more accurate analysis of the error.

About your error .. This looks like file permission.
If you use command line use:

Chmod 0644 /wp-admin/admin-ajax.php

If it does not resolve, you should use the command below. But note this command should be changed soon after by the aforementioned (chmod 0644).

Total Permission Command:

chmod 0777 /wp-admin/admin-ajax.php

Like I told you after making your changes. Go back to chmod 0644.

Search about File Permissions and will understand that chmod 0777, should be avoided at most.

Do not forget to always before and after major changes …
You should do a full backup. That is, files + database.

If you are not using the command line.
Go through the File Manager and look for the file permission change option. Change only what you are sure.
You can use the numbers above. Without the >> Chmod.
0644 or 0777

On the media files, I believe it’s the same permissions problem …
In short, you should as STANDARD put to:

PASTES AND SUBPASSES chmod 0755 or 0755 (in the directory)
Files chmod 0644

Only Folders and Files that Need Recording Continue …
Chmod 777 (But it is not advisable)

This depends a lot on your server. Then consult him to find out the correct permission. It can be Chmod 0700 // 0744 (Search)

Since you are learning …
I’ll give you some tips …

Always keep in mind the Web Server. This is not your machine, but the software that manages your websites.
It’s usually Apache. So keep in mind that when you are looking for details about errors or doubts always insert the Web Server as a reference.

Ex: wordpress + NGINX (Apache) + Error / Doubt

This will help you …
Another important fact is to focus on the mistakes is as I said above, analyze the LOGS. Be it WordPress or your Web Server.

I hope I have helped you.