If device is on and nobody home notifications to cell phone

Is there any easy way to do it? And also to add exeptions for some devices. Moreover I am speaking about lights and switches.

It happend to me quite some time that my one of the Yeelights are turning on and of randomly

Okay so I was informed that somebody in house reseted electricity few times in a row resulting in all Yeelight bulbs were on. Any Idea how to prevent it please?

Ahd how I can display in logger only “Home assistant started” event?

At first set up your devices to start turned off when powered up/restarted.
It should be rule of thumb for bulbs/lights. It likely will be opposite for smart sockets - but it’s not your case

Then you can write automation. It’s easy in NodeRed. the same about sending push notification to your mobile everytime HA is restarted.
Both should be possible using native HA automation but I don’t know how. I can bet it will be more complex though