or just simple application to receive alerts and check status, statistics of the test, acknowledge test status on iPhone?
Yes, it can be done just nobody knows when exactly.
Meanwhile HostMonitor may send messages to Viber, Telegram, Slack..
For me, it would be iOS, both iPad and iPhone.
But a 'mobile friendly' web application might be more feasible and serve more mobile platforms at once.
I find the current web interface is kinda usable on an iPad 10inch or more, but on the iPhone it is way too tiny and fiddly to actually work with.
In terms of actual functionality, I haven't given it too much thought yet, but if there's any chance of it becoming real I would be more than willing to give my input on that.
There is Compact Web Interface
Quote from the manual
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Also, there is version of the interface designed for mobile devices with a low resolution screen.
To access this service use the following links:
http://webservice_address/compact.htm
http://webservice_address/tiny.htm
http://webservice_address/links.htm
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Can be used on any phone (with web browser of course)