"Electron has -ve charge,proton has +ve charge,neutron has no charge."
But actually what is charge?
"unlike charges attracts each other"
Do +ve charge attract -ve charge to itself or -ve charge attract +ve charge to itself?
The "what is charge?" question unfortunately doesn't have a good answer at the moment. We know that a coupling constant related to charge appears in the quantum electrodynamics Lagrangian (if that means anything to you), and that this causes electromagnetic interactions. But ultimately charge just seems to be an immutable quantity that all fundamental particles (e.g. quarks and leptons) are born with, which causes them to interact.
As to your second question, there is a good answer. The answer is that the positive and negative charges will exert equal and opposite forces on each other. This is necessitated by Newton's Third Law, which states that for each action force there must be a reaction force. Remarkably, this classical law deduced from observations on the macroscopic world holds even at the subatomic level, and is true even in cases of quantum interactions.
The universe is inherently imbalanced or in other words wierd because things exist in it. If you think about it for a minute, it would make a lot more sense and be a lot easier to explain if there were no universe at all, but things exist, meaning that unless they are somehow topologically equivalent to nothingness (which i'm pretty sure is impossible) are fundamental, which means that there is no real 'explanation' as to what they are other than that they are themselves. what is 1? what does the number 1 mean? Well, it means 1. It doesn't need any more explanation than that, and no more can be given.
Charge is probably the same way, and if it isn't, whatever makes up charge probably is.
What is mass? You can say that mass is: "A resistance to a change in motion." The same definition may hold true for like-charges; the definition of charge--when involving two particles of the same charge--is that there will be an equal and opposite reaction if both are brought close enough together. A similar argument can be made for unlike charges. Keep in mind that in order to define charge, you must consider at least two charged particles; not one.
The ability to interact w/ virtual photons still isn't quite satisfying. I've heard some Kaluza models and extra dimensions in string theory posit that properties such as charge can be thought of as momentum along an extra, compactified dimension.
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