(a) The electron would not move in circular orbits.
In a system with two protons, the electron doesn't orbit one proton in a simple circular path like in a hydrogen atom. Instead, it moves in a complex path influenced by both protons, forming a linear combination of states in molecular orbital theory. This statement is true.
(b) The energy would be \(2^{4}\) times that of a \(\text H\)-atom.
This statement is mathematically inaccurate. In an ionized \(\text H_2^+\)​ molecule, the energy levels are different from that of a hydrogen atom, but the relation mentioned here doesn't hold true.
(c) The electron's orbit would go around the protons.
 The electron is shared between the two protons, forming a bonding molecular orbital that involves motion around both protons (similar to a covalent bond). This statement is true.
(d) The molecule will soon decay into a proton and an H-atom.
The ionized \(\text H_2^+\)​ molecule is unstable and can break down, typically decaying into a proton and a neutral hydrogen atom (H) through recombination.
Hence, option (2) is the correct answer.