Question

Can matter be converted into energy?

Answer 1

Energy and matter are connected according to special relativity and this has been experimentally demonstrated. It is the famous formula:
$E=m{c}^2$, where m is the relativistic mass and c the velocity of light. or
$E^2=m_0^2{c}^4+p^2{c}^2,$ for a particle with rest mass $m_0$ moving with momentum p,
The rules of transformation follow Quantum Mechanical solutions of kinematic and potential problem equations.
Annihilation is one way to transform matter to energy.
Yes
Fission is another (when splitting an atom, what happens to its two parts?)
In the quantum mechanical description of nuclei, they are represented by potential wells with energy levels, some filled. The number of baryons (protons and neutrons) bound in this potential well characterize the nucleus. Nucleus A that is struck by a neutron (for example) becomes a nucleus B higher up in baryons by absorbing it into an energy level of this level of this potential well. In fission this higher up nucleus is unstable and falls into a lower energy state, giving up part of its mass in energy according to the relativistic formulae, and breaking into smaller nuclei and free neutrons which go on to sustain the fission on another original nucleus. Generally, a form of fission happens if a nucleus is unstable.
There is also fusion, two deuterium nuclei adhering at a lower energy level and giving up energy.
The binding energy curve shows whether nucleons can fuse or fission and give up as energy a part of their mass.