We present a first-principles density functional study elucidating the effects of solvent, metal ions and topology on the electronic structure and hydrogen bonding of 12 well-designed three dimensional G-quadruplex (G4-DNA) models in different environments. Our study shows that the parallel strand structures are more stable in dry environments and aqueous solutions containing K(+) ions within the tetrad of guanine but conversely, that the anti-parallel structure is more stable in solutions containing the Na(+) ions within the tetrad of guanine. The presence of metal ions within the tetrad of the guanine channel always enhances the stability of the G4-DNA models. The parallel strand structures have larger HOMO-LUMO gaps than antiparallel structures, which are in the range of 0.98 eV to 3.11 eV. Partial charge calculations show that sugar and alkali ions are positively charged whereas nucleobases, PO4 groups and water molecules are all negatively charged. Partial charges on each functional group with different signs and magnitudes contribute differently to the electrostatic interactions involving G4-DNA and favor the parallel structure. A comparative study between specific pairs of different G4-DNA models shows that the Hoogsteen OH and NH hydrogen bonds in the guanine tetrad are significantly influenced by the presence of metal ions and water molecules, collectively affecting the structure and the stability of G4-DNA.