Stop Zabbix notification for nodes under zabbix-proxy when proxy service is down

Create user accounts for all the receivers, add corresponding media entries (emails) to them. Configure actions as usual, but place all of these users in a common usergroup that has "Frontend access" set to "Disabled" - this way they will be able to receive notifications, but not log into the frontend.

Alternatively, have a single user account with multiple user media entries for all the email addresses.

Your question is not 100% clear, so I've covered both possibilities:

If you want to check whether data is not arriving from the Zabbix agent, use the nodata function.

Returns:
1 - if no data received during period of time in seconds. The period should not be less than 30 seconds.
0 - otherwise

For example, a trigger which will fire if no data was received for 10 minutes:

{mysql.query.nodata(600)}=1

If you want to check whether the value has not changed, use delta.

Returns the difference between the maximum and minimum values in a period ('max()' minus 'min()'). The period is set in seconds or as a number of collected values (preceded by a # hash mark) in the first parameter.

For example, a trigger which will fire if the value has not changed for 10 minutes:

{mysql.query.delta(600)}=0

Finally, you probably want to rename your item. mysql.query is very generic, and is already used by common MySQL templates. Something like aggregator.highest_click_id might be more appropriate.