Determining aromaticity of compounds
(i) that's correct

(ii) is aromatic, it fit's the 4n+2 rule with n=1.  Here is a drawing of furan showing 2 lone pair electrons in a p-orbital that completes the cyclic aromatic ring. Furan's other lone pair of electrons is perpendicular to the pi system and does not play a role in furan's aromaticity.



(image source)

(iii) Edit to incorporate @jerepierre's comment:

Just like phenol can exist in equilibrium with its non-aromatic tautomeric keto form



so can derivatives of pyrimidinedione (or uracil).  However, unlike phenol were the equilibrium lies far to the aromatic phenol side, these compounds usually (it depends on the substituents) exist in the keto form.  The strength of the keto and amide bonds outweigh the weaker aromaticity of the pyrimidine skeleton and shift the equilibrium to the keto side.



(image source)

The question remains, is the keto form aromatic?  As jerepierre points out, you can draw the following resonance structure for the keto form.  In this double-dipolar resonance structure there are 6 pi electrons 2 in the double bond and 2 [a lone pair] on each nitrogen) suggesting that this resonance structure would be aromatic.  Since this resonance structure contributes to the overall description of the molecule, it would be fair to say that this molecule has some aromatic character; certainly not as much as benzene or furan - but some.