a. `A = Me_(3)C--O--Me_(3)` (Di-t-butyl ether)
`Ag^(o+)` reacts with `Br^(o+)` leaving `Me_(3)C^(o+)` which reacts with `CO_(3)^(2-)` to give `Me_(3)C--OCO_(2)^(-)`. The latter loses `CO_(2)` leaving `Me_(3)CO^(-)` which reacts with `Me_(3)C^(o+)` to give the product. Due to steric hindrance, the yield is less.
Mechanism :
b.
c.
d. It is an example of Friedel-Crafts type addition to a double bond.
e. It is an example of organometallic coupling reaction.