Think of it like starting a new job. You're really nervous in the beginning and overwhelmed learning everyone's names and how to use the photocopier or whatever, but after 6 months you're comfortable and have it all under control. This will be the same - it's only scary because it's unfamiliar.
How often do you actually have power cuts that last more than a few seconds or minutes? I think I've had one that lasted more than a few minutes in ten years and it was during the day!
I vaguely recall being worried about powercuts too when I first started living alone and putting torches in every room. I have no idea why I was so concerned about it. It rarely happens and when it does it's not a big deal. (Your phone must have a torch?)
If you get a key safe it should meet the right standards including Secured by Design police spec and be correctly installed, otherwise you're just making yourself vulnerable.
Car maintenance - you just need regular service at a trusted garage plus breakdown cover. Halfords do winter vehicle health checks. If you have the car manual it will tell you how to top up washer fluid, what pressure the tyres need to be etc. If you don't have the manual, Google will tell you.
House maintenance - if it's rented then landlord should sort anything with the property that breaks and arrange boiler service.
I did a basic plumbing course when I started living alone which demystified it all and explained the difference between an emergency leak that needs a plumber and a non-emergency leak you can sort yourself at your leisure. Plus stopcocks and basic repairs. It's not scary once you know that.
You can look most things up between YouTube, the Screwfix forums and general Google.
He may have made you feel helpless or incapable, but you'll soon realise you can handle the car/house maintenance yourself just fine. Most of it isn't that difficult, the rest you outsource (like everyone else, including him).