Anything that you rely on in a situation like that should be 100% maintenance free and should not rely on technology more complex than what you can make today in your garage with hand tools. Go over that level and it will just buy you a little bit of comfort but it won't last.
Candles: yes. Solar panels+batteries+inverters: forget it. Even a basic charge controller would be a major feat of engineering under those circumstances. I have some ideas on how I'd make that work if I really had to but I'd probably be too busy defending myself from marauders and taking care of my crops to be able to work on it...
What's interesting here is that plenty of the stuff that we take for granted is absolutely state-of-the-art engineering and there is no way that you'd be able to continue to rely on it for more than the available stock that you could still lay your (likely very grubby) hands on for spares, and even those have a limited shelf life.
Bootstrapping to the present day level of technology where working semiconductors can be taken for granted will take a long, long time. Even if you have the knowledge. Assuming that enough of the eco-system survives that you will be able to survive and procreate I'd estimate at least several generations, if we didn't entirely regress to some more primitive state. Mad Max would be an amazing level to bootstrap from, having working computers means you're focusing on the wrong thing. Electric light might be a good idea, but personally I would not count on LEDs or bulbs to last long enough in quantity and if you're going for batteries keep it simple: lead acid flooded cells (You'll need some basic chemistry tools and materials to make sulphuric acid, but that's probably doable).
It would be an interesting hard sci-fi novel to see the village black smith replaced by the village semi-smith and wind mill replaced by the nuclear mill.
Yes, if you rely on a bunch of hard to obtain tech, a stable energy supply, relatively pure starting chemicals and a whole pile of tooling. I'm aware of Jeri Ellsworth and Sam Zeloof, both are off the charts smart and capable and put the lie to the 'relatively easily' for anything approaching usable devices in quantity.
You'd be better off to learn how to wire relays, assuming you're going to find enough power. It's much easier to get to reliable logic circuitry via that route than it is by homebrew semiconductors, that's an optimization that you can do without if you have nothing. Even tubes would be simpler. And much, much easier to make. Nothing that you couldn't do with early 1900's technology.
Nuclear power in such a situation will likely only kill the operators. Wind power could be relied on for many decades, the Jacobs Wind Electric powerplant that was installed in the arctic still worked decades later under some of the most harsh conditions on the planet. Keeping it simple is key to anything that needs to work in such a setting.
Some electricity some of the time is very useful compared to no electricity, ever.
Lithium batteries will indeed likely not last for a decade but that has nothing to do with solar installations, though you could combine them (but you'd have a choice of chemistries and for stationary installations where weight and size are not usually the limiting factors you can do better than Lithium).
Usually the case is that one cell in a 'dead' battery has far lower capacity, and might only run a flashlight for 20 minutes (which is still useful, though I dispose of those). The other cells are comparable to new ones in capacity (maybe they're 90% or whatever of their original).
We often have a distorted idea of lifetimes and reliability because absent real scarcity we're overly prone to discarding things which can be fixed (e.g. using 5 bad laptop batteries to make four good ones) or are still usable. If you have no other source of light at night a flashlight you can only use for 20 minutes is still a life changing transformative device.
One could imagine searching for battery technology with much longer lifetimes. But I think you'd be better off with the best batteries you can find out of thousands of lithium cells ambient around you than just a few 'super batteries', esp if you're only talking about your lifetime or the lifetime of your children.