I was reading this answer and I saw an energy diagram:
Does the energy belong to the system or to the outside?
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The big arrow labelled energy is just an axis. It's supposed to indicate the upwards is positive, i.e. energy is being added to the system, and downwards is negative, i.e. energy is being emitted from the system.
Re the extra question:
where does the energy released in a nuclear reaction go, is it kinetic energy or heat?
Heat is a collective phenomenon. It doesn't make sense to ask about how much heat a single object has. At the individual particle level all reactions produce either photons or kinetic energy. In the latter case the energy is released as the kinetic energy of the reaction products. There is a discussion of this in my answer to Can we make usable energy from subnuclear particles?.