Note that no other reagents are needed in order to complete any of these sequences, you should only be using what is there.
Work in progress, at this time only links to similar examples are available, more detailed / specific answers will be posted as and when time allows.
Part A:
i. This is an example of the Baeyer-Villiger reaction.
ii. Friedel-Crafts alkylation of benzene via an electrophilic aromatic substitution including a carbocation rearrangement via an 1,2-alkyl-shift.
Part B:
i. The two key steps are examples of electrohilic aromatic substitutions of the benzene . In the first substitution, the electrophile is the C in the carbonyl of the ketone (activated by protonation first) and it's an example of nucleophilic addition to the ketone (weak nucleophile, so acid catalysed). In the second substitution, it's a substitution of an alcohol (acid catalyst required to make the -OH into a better leaving group: SN1). In both aromatic substitutions, the electron donating -OH group directs the reaction to the para-position.
ii. An example of a nucleophilic addition to the aldehyde. Similar in some ways to the Wittig reaction. The nucleophilic P of the triphenylphosphine attacks the CBr4 in an SN2 with loss of Br-. The ylid is formed when either Br- or PPh3 removes a second Br group from the CBr3-PPh3. The ylid then reacts with the carbonyl in a Wittig type process.
Common general errors: (1) Ignoring reaction conditions i.e. effect of acidic or basic environment (2) poorly drawn arrows, e.g. not starting at the Nu site (3) backwards arrows (4) wrong use of arrows e.g. resonance (5) not showing formal charges (6) missing arrows esp. when adding or removing H+ (7) compressing several mechanistic steps into a single step.