(i) increases the rate of reaction «and is not used up» ✔

provides an alternative pathway with a lower activation energy / a greater proportion of collisions have energy greater than the activation energy ✔

(ii) ultraviolet light / UV «radiation» ✔

(iii) the lone pair (negative charge) on the oxygen of $\ce{HO-}$ attacks the carbon bonded to Br, shown by a curly arrow running from that lone pair to the carbon ✔

a second curly arrow runs from the C–Br bond to the Br atom as it leaves ✔

the transition state «in square brackets» carries a negative charge and shows the partial bonds HO···C···Br ✔

$\ce{CH3CH2CH2OH}$ forms as the organic product, together with $\ce{Br-}$ ✔

(iv) Number of signals: 4 ✔

Chemical shift ranges: 0.9–1.0 «ppm, CH3» AND 1.3–1.4 «ppm, middle CH2» AND 3.3–3.7 «ppm, CH2–O» AND 1.0–6.0 «ppm, OH» ✔

Integration traces: 3 AND 2 AND 2 AND 1 ✔

Splitting patterns: triplet «CH3» AND multiplet / sextet «middle CH2» AND triplet «CH2–O» AND «broad» singlet «OH» ✔

(i) M1: increases the rate; M2: lower activation energy through an alternative pathway, or more particles with energy at least equal to the activation energy. (ii) [1] for UV light; accept sunlight or heat; do not accept light alone. (iii) M1: arrow from the nucleophile's lone pair to C; M2: arrow from the C–Br bond to Br (accept it drawn in the transition state); M3: transition state with partial bonds and the negative charge; M4: both products. Award [3 max] for an SN1 mechanism; do not award M3 if a full HO–C bond is drawn in the transition state. (iv) [1] for each line: number of signals, chemical shift ranges, integration, splitting; accept the signals in any order; accept any three correct details for a single signal for [1] each; accept 'multiplet' for the middle CH2.