Energy is not the same thing as photons. They can be converted between each other, but they’re fundamentally different things: energy is just a real number, and photons are particles with momentum, spin, and so on. For a given process, energy is conserved; the total energy of the system before the interaction is the same as the total energy after it. That energy can show up on the “balance sheet” of the process as additional particles, but there’s no reason why they have to be photons in particular. In beta decay, for example, a proton decays to a neutron and an electron, with a neutrino around to conserve momentum. The binding energy of the atom changes, but it doesn’t involve photons. (Since we’re talking about decay here, I should also mention that beta decay doesn’t imply that the proton is composed of a neutron and an electron, or that it somehow has a neutron and electron sitting inside it. What’s going on is that a W boson changes the one of the quarks in proton from an up quark into a down quark, then decays into an electron and neutrino.)
There are reactions of the form γγ-> qq* (that q* should be \bar{q}, an antiquark), but I don’t think that’s the way it’s done in practice when physicists are trying to study quarks. As for why such a process should exist, it’s just the reversal of an particle-antiparticle annihilation process.
There’s also the theory that God has been running multiple simulations of multiple universes, to see how they turn out and which one would be the most feasible, before He goes and actually creates a universe. The entire “universe” that we think we know is, in actuality, just one of those simulations.
The usual oversimplified image of forces inside a nucleus is to picture a hill made out of foam rubber. Place some heavy stuff (nucleons) onto the top and they make a dimple* at the top which holds them and keeps them from rolling away.
While the protons would love to separate and roll down the hill, the dimple holds them in. Assuming that the forces (ratio of protons-neutrons) and other stuff** work out right. Else you get decay or fission.
Note that rolling nuclleons up the hill and over the edge takes energy. Plus pushing the dimple down takes energy. It’s springy. You get the energy back during decay or fusion.
Well, okay. Not always. Curve of binding energy and all that. Like I said: oversimplified. You can try to save things for “light” elements by talking about the bottom of the dimple being lower than the bottom of the hill, so for light elements you get net energy by rolling stuff over the lip of the dimple and down into the deep dimple. And at some point around here the analogy starts to get stupid.