Step 1: Identify the molecule.
Furan is a five-membered aromatic heterocycle with formula $\text{C}_4\text{H}_4\text{O}$.
Step 2: Recall what a heteroatom is.
A heteroatom is any ring atom that is not carbon.
Step 3: Locate furan's heteroatom.
Four ring positions are carbons and the fifth is an oxygen, so oxygen is the heteroatom.
Step 4: Count the double bonds.
Around the ring there are two alternating carbon-carbon double bonds.
Step 5: Check the aromatic electron count.
The two C=C bonds supply 4 electrons and one oxygen lone pair adds 2 more, giving the $6\pi$ aromatic sextet, which confirms the structure.
Step 6: Reject the other choices.
Sulphur and nitrogen are not present, and the count of double bonds is two, not one, so options with S, N or only one double bond are wrong.
Step 7: State the pair.
Furan has oxygen as the heteroatom and 2 double bonds, which is option (2).
\[ \boxed{\text{Heteroatom = O, \ double bonds = 2}} \]