Bonding water

Answer number one is true, as the Hydrogen molecule receives one more electron in the $s1$ orbital, causing it to reach the configuration of $2s1$ , that of helium. By looking at the above Lewis Dot Diagram, we can tell that the oxygen molecule is satisfied with eight electrons, satisfying the octet rule. However, the bond between hydrogen and oxygen is a single bond, because each of them donates one electron to the shared system. In covalent bonding, one accumulated shared electron pair corresponds to one bond.

Since the valency of a hydrogen atom is 1, it cant form a double bond with any of the other elements, however oxygen could. But since oxygen is bonded to 2 hydrogen atoms, both the bonds will be single bonds.

I understand where you're coming from, but technically the hydrogens IN A WATER MOLECULE do not have the same electron configuration as Helium because the orbital is a hybridised sp orbital, and so is a different shape to the 1s.

To be elementary (pardon the pun) an oxygen molecule needs 8 electrons in its outer shell. To have this it must share 2 electrons with the 2 hydrogens (one each as it is H2O). This means each hydrogen atom shares one electron with the oxygen. Furthermore, hydrogens can't form a double bond or triple bond - they only have one valence electron.