To state the obvious, since you are using a latter version of PHP, it is expected that some functions / constructs that were perfectly fine in previous versions of PHP are now considered deprecated.
However, since they are still viable functions / constructs, they work just as fine as before.
As a developer, whenever I see those warnings, I know I have to make modifications for the program to continue working with future versions of PHP.
The second notice message is thrown by standard joomla "Content - Contact" plugin. The plugin is looking for a field that is not provided by Custom Properties result items.
The plugin assumes that the field exists instead of checking for its existence before using it.
If you want to mute that error you can disable the Content - Contact Plugin.
(I see what I can do to "please" that plugin in a future version of Custom Properties)
In general, you should configure your hosting to not display 'Deprecated' warning messages, unless you are developing your own extension with consideration to forward compatibility.