What is the $IUPAC$ name of mesityl oxide?

Provide the $IUPAC$ name and structure for the following compounds:
$(i)$ Propanone
$(ii)$ Butanone
$(iii)$ Hexan$-3-$one
$(iv)$ $2,4-$dimethylpentan$-3-$one
$(v)$ Pentan$-3-$one
$(vi)$ $2-$methylcyclohexanone
$(vii)$ $4-$methylpent$-3-$en$-2-$one
$(viii)$ Benzophenone
$(ix)$ Acetophenone
$(x)$ $3-$methylbutan$-2-$one
$(xi)$ $5-$hydroxy$-5-$methylhexan$-3-$one
$(xii)$ $3-$oxobutanoic acid
$(xiii)$ $3,3-$dimethylheptan$-2,6-$dione.

Which of the following is correctly matched according to their common names?

Which of the following is a mixed ketone?

How many total ketones are possible for the molecular formula $C_5H_{10}O$?

Give the structures of the following compounds:
$(i)$ $4-$Nitropropiophenone
$(ii)$ $2-$Hydroxycyclopentanecarbaldehyde
$(iii)$ Phenyl acetaldehyde