1. Circular Orbits (a): The Bohr model's concept of fixed circular orbits applies only to single-electron species with a single nucleus (like H, He⁺) where the force is central . In an ionised H-molecule (H₂⁺), the electron moves under the influence of two nuclei (two protons). The force field is not central, so the electron cannot move in simple circular orbits. This statement is correct.
2. Energy (b): The energy of the ground state of H₂⁺ is approximately -16.3 eV, which is lower than that of a hydrogen atom (-13.6 eV) due to bond formation, but it is certainly not $2^4$ (16) times that of a H-atom. This statement is incorrect.
3. Orbit around protons (c): According to the quantum mechanical model and Molecular Orbital Theory, the electron probability density (molecular orbital) encompasses both nuclei . Qualitatively, the electron 'cloud' surrounds both protons. This statement is correct.
4. Decay (d): The H₂⁺ ion is a bound, stable species in its ground state (similar to how H₂ is stable ), so it will not spontaneously decay into a proton and a H-atom. This statement is incorrect.

Therefore, statements (a) and (c) are correct.