Jim M

Sounds like something is not quite right with Javascript or the theme on your community since upgrading. Either there is a theme compatibility issue, cache issue, or a write issue on the server. I would recommend clearing cache by going to ACP -> System -> Support. Then try again.
If that does not help:
Switch to an unmodified theme and check again. Check to ensure write permissions on your server are correct. If you're on our Cloud, please submit a ticket as we would need to see what else is going on.

There is no delete all messages button, I'm afraid. To delete a status update, you will need to click the status update and view it. You can do this by clicking the status update in the block or going to the profile of the user who posted it. You can then delete it by clicking "Options" then "Delete" as outlined below in the screenshot.
Moderator permissions control what you can moderate on the front-end of your community, such as here. You will need to ensure your group has correct moderator permissions. Administrator permissions control what you can do in the Admin Control Panel so simply because you have an administrator account does not mean you have moderator permissions. For more on this, you can read the following Guide: https://invisioncommunity.com/4guides/staff-and-moderation/creating-administrators-and-moderators-r31/
 

There is not a separate mobile view in our software as a responsive architecture is used (aka we adapt the view based on screen-size). CSS loads for a whole page regardless of what screen-size is used. You would need to use media queries to specify what parts of your custom CSS should render for certain screen-sizes: https://www.w3schools.com/Css/css_rwd_mediaqueries.asp

This warning in your ACP is a strong recommendation as these functions can be dangerous but our software can run without issue with them enabled. This is merely a recommendation to strengthen the security of your server as our software (and others) does not utilize these dangerous functions (as mentioned in the warning). If you are on a shared server, you may not have complete control over the server as indicated by your hosting provider. This would be something you would want to research if you want the capability to better secure your server or stick with your provider.