Reaction mechanisms for set of given reactions

Question

Please assist in drawing full reaction mechanisms for the following reactions:

(reagents shown in italics, where having)

a) propanoic acid + CH₂N₂ ---> methylpropanoate + N₂

b) benzoic acid ---trifluoroacetic anhydride---> benzoic trifluoroacetic anhydride

c) benzoic trifluoroacetic anhydride ---CH₃CH₂OH---> ethylbenzoate

d) benzaldehyde trichloride ---^-OH/H₂O---> C₆H₅COO^- + HCl₃ (I suppose this is one theoretical)

e) diphenylethane-1,2-dione ---1. NaOH, H₂O/2. H₃O⁺---> 2,2-diphenyl-2-hydroxy acetate

f) 2,2-dimethyloxirane ---H₃O⁺---> 3-methylbutanal

Answer 1

d) is the last stage of the haloform reaction. You can look this up.

f) Answer hampered by image size restrictions, but here are the key steps: