I'll preface that what I'm gonna say is mostly opinion but I'll share what I've experienced so far. I'll try to share some points of concern for you to consider just so you know what you will need to keep an eye out for while injecting co2.
But a lot of concerns that you have at the moment mainly hinge on scenarios where folks try to walk the razors edge and dump an enormous amount of co2 trying to compensate for ridiculously high lights or demanding plants. Since I don't think that you will be injecting co2 to those extremes at the start, you wont be posing any issues pertaining to your fish. But very generally, as long as you monitor your fish whenever you make co2 adjustments, you shouldn't have a problem.
My main advice is to take things slowly and make small incremental adjustments over time. Since you sound quite experienced I'm sure you'll see major improvements even with the tiniest amount of co2. A little will go a long way if you can create favorable conditions.
1. If you can provide your specific gh/kh parameters we'll have a better idea on what kind of issues you should look out for but yes, co2 will affect all three one way or another. Since co2 is acidic, driftwoods and certain stones can raise or lower gh/kh as they are being dissolved in the water.
Understanding the relation ph/gh/kh and how they work together is important but kh should be your first concern of the three. You'll find ph fluctuates throughout the day which is normal but the lower the kh of your tank is, the more prone you are of dropping your ph too low. Ideally you would want some kh, at least 3dKh to give you some room for mistakes.
The kind of fish you have will also dictate how much co2 you can inject into your system. Introducing co2 slowly would be key to allow your fish to acclimate to the adjustments.
2. As said before you do run the risk of gassing your fish but it mostly happens if you are carelessly cranking the co2 or if you buy a low quality regulator.
You'll hear 30 ppm co2 as a benchmark of how much co2 you should have in your tank but its not really a good measurement. Aiming for the 30ppm range especially when you are new is where you'll start getting into trouble. Unless you are trying to grow the absolute most demanding plants, you'll have good success with even half that amount.
But if you are so inclined you can find ph/kh/co2 charts online or use a drop checker for co2 measurements but understand each of these tests have their own pitfalls that only tell you half the story. There are so many interactions happening in your tank that its hard to account for factors than will skew test results. Personally I think you are far better off looking at the response from your plants and fish instead of trying to chase numbers.
A few things you should consider is that temperature plays a role in how well gases can be dissolved into water. Warmer water can hold less o2/co2 than it can when its colder.
Circulation is much more important than a high concentration of co2. Co2 is useless if you don't have an adequate delivery system to transport co2 and nutrients around the tank.
Good surface agitation allows for gas exchange that helps prevent co2 building up to a lethal level. Keeping in mind that you can kill your fish with co2 poisoning even if your plants are pearling and you have high oxygen saturation.
3. If your regulator is hooked up to a solenoid, then I wouldn't ben concerned about power outages. I don't even think your plants will be affected by a blackout for a few days since your plants won't need co2 if lights are off. Now if your power is out for like a week you might get a little melting but you'll be back on track in no time with co2.
You may not even need it, but having an air pump that can plug into a power bank would be nice to have in case.
Sorry if I'm being way too elaborate but the last thing I want to be is vague/unclear in this matter. I'm not trying to scare you in anyway just share some issues I ran into. Definitely take everything I said with a grain of salt and use my topics to direct you in areas you should research. I'm pretty biased on some of my points and may very well be wrong but my goal is for you to know what to look into so you can come to your own conclusions. I'm sure you know by now how hard it is to parse through information online.
If you haven't already, it might be fun to document your progress in a journal so we can all follow along. Good luck!