Connecting flight anxiety

[StressedEric]

I am flying on my own with my kids for half term to cyprus via vienna as it was the most convenient flight times. The flights are london to vienna, then an hour or so wait, then flight to Cyprus. On the return flight there is only half an hour between the two flights.
I am anxious about this as have never done a stop/ presume plane change in another city en route, I have always flown direct before. My kids love flying so I am not worried about anything apart from the logistics of connecting flights.
Can anyone tell me how it works ?
Do I have to collect bags at Vienna and go through passport/check in again.

What happens if one bit of the flight is delayed which means I miss the next one ?
How is a 30 minute gap between flights going to work ? Surely it will take me that long to get us all off one flight, let alone board another one at presumably a different gate/part of airport.
Will our bags actually make it with us ? We all have cabin bags so will pack those to the gunnels I think and only put stuff in the hold suitcase that we could manage without just about.

Thanks !

Updating ! It worked, just about.

Outbound, it was good to break up a 5 hour flight with a walk round the airport and a leg stretch. I would do a 1.5 hour layover again.

inbound, plane took off on time and landed on time thankfully. We made it just onto the London flights from Vienna. Whoever said " run" was accurate. It was very stressful tbh and whilst it worked, it was not pleasant.
As you all predicated, our checked bags did not make the connecting flight and we had them back the next evening ( they were on the first flight out of vienna the next morning) and whilst I could track via my AirTag, I also had decent info and live tracking from Austrian/LHR.
Thanks for your advice, much appreciated.

I'm glad it worked! I couldn't deal with the stress of that but I'm of the 'want to be at the airport 4 hours before train of thought'