Upgrading Drupal

This is the second time in about a month, that I needed to update my Drupal 8 installation with some "security" fix.

I have not used Drupal before. I was not a Drupal 7 developer guru. I found that in order to use Drupal, you have to have all sorts of background, including development in Drupal 7, Symfony, and who knows what else.

Hello,

   I just upgraded to 8.6.10 from 8.6.1 using composer. I also ran update.php.  Running composer oudated "drupal/*"  now returns nothing. The problem is when I go by to my website and view the status report it still shows 

Not secure! (version 8.6.10 available)

Hello, 
After an update to version 8.6.10, I no longer access the site....
I did a manual update
I made an update.php that updated the database, but without success.... Can you help me?

I have these errors : 

The website encountered an unexpected error. Please try again later.
Error: Class 'Drupal\Core\Cache\Context\RequestFormatCacheContext' not found in Drupal\Component\DependencyInjection\Container->createService() (line 262 of core/lib/Drupal/Component/DependencyInjection/Container.php).

I've done a base install of Drupal 8.6.9 on IIS 10 with PHP 7.3.2 and MYSQL 5.7 (IIS rewrite module also). It worked fine. The following day I decided to upgrade patch to 8.6.10 following the usual instructions of deleting everything but your "sites" folder and copying in the new patch files. I then proceeded to run http://localhost/drupal/update.php. The first update page displays fine.

I'm planning to do my first core update from version 7.59 to 7.63.
I've tested it already on a non-production web site, and it seems to work fine.
I will take a full file and a database backup before the production update. How should I proceed with the restore if something goes wrong ?
I would need an exact action plan to be on the safe side.

Thanks,
Eva
 

I was actually surprised at how easy it was to follow the directions and manually upgrade Drupal.  All went well, and in 10 mins the site was up and running again. 

However, I'm just noticing that ONE LONE PAGE seems to be totally completely dropped off the site, except for the text.  It has nothing on it, no theme, no header, the source code when I look at the page is just two lines within <p> tags.