Deduction of the compound's structure:

• The carbonyl compound $\text{C}_3\text{H}_6\text{O}$ could be either propanal (an aldehyde) or acetone / propan-2-one (a ketone).
• Because it does not reduce Tollens' reagent, it is not an aldehyde; hence it must be acetone ($\text{CH}_3\text{COCH}_3$).
• Acetone contains the carbonyl group ($\gt \text{C=O}$), so it reacts with hydroxylamine to form an oxime: $(\text{CH}_3)_2\text{C=N-OH}$.
• Acetone possesses a methyl ketone group ($\text{CH}_3\text{CO}-$), so when treated with iodine and aqueous sodium hydroxide, it undergoes the iodoform reaction to form a yellow precipitate of iodoform ($\text{CHI}_3$).

In the gaseous phase, there is no solvation effect or steric hindrance due to hydration. The basic character of amines is determined solely by the electron-donating inductive effect ($+I$ effect) of alkyl groups. The greater the number of methyl groups, the higher the electron density on nitrogen and the more readily it accepts a proton:

$$3^\circ\text{ amine} \gt 2^\circ\text{ amine} \gt 1^\circ\text{ amine} \gt \text{NH}_3$$ $$(\text{CH}_3)_3\text{N} \gt (\text{CH}_3)_2\text{NH} \gt \text{CH}_3\text{NH}_2 \gt \text{NH}_3$$

Analysis of statements regarding order of reaction:

• By definition, order is the sum of the powers of concentrations in the rate law expression (correct).
• Order cannot be predicted directly from the stoichiometric coefficients of a balanced equation for complex/multi-step reactions; it is only equal to stoichiometric coefficients for simple elementary steps. Therefore, stating that order is 'always equal' to the sum of stoichiometric coefficients is incorrect.
• The order of a reaction can be zero, integral, or fractional (correct).
• The order of a reaction is strictly an experimentally determined quantity (correct).