Your questions are all valid, but the topic is tricky.
"allowing access to minors" is a very broadly interpreted term. Basically it's a catch all that they can nail you for if a minor gets a hold of your guns no matter what you do. If you buy a small gun safe, lock up your guns in it, then put that smaller safe in a bigger safe and lock that, and a kid gets into it using a cutting torch and a block of C4, they can still bust you for it.
Does it violate "treat every gun as if it were loaded?" No, because you aren't supposed to have them loaded in the safe anyway. In fact, guns and ammo should always be stored in separate places.
Would not having one increase the chances of an intruder stealing them? That all depends on if an intruder finds them. I've got a small arsenal in a big floor standing safe. I'm pretty sure if someone broke in they'd find the safe, since it's the size of a fridge. If I hid the guns throughout the house, there is a better chance one or more would not be found. On the other hand, even though they can find the safe, they'd have a heck of a time hauling it out of the house.
My feeling is that if you just have a couple of guns, and they are primarily for home defense, your strategy may not include gun safes. As I said I have a safe that holds my weapons, but I also have a couple that do not live in the safe that I use for home defense. The only time the home defense weapons go in the safe is when visitors are coming over.
There are other options rather than large safes. They make inwall locking cabinets for holding shotguns that fit nicely into a stud cavity behind a door, and they make small pistol safes that pop open automatically with a fingerprint swipe or by laying a hand down on them and tapping the combination with your fingers.
Cost of the safe should have been something you considered before laying out the money for guns. Now that you have them, you need to invest what it takes to keep them safelty and responsibly.
