For (a), there is no doubt that there will be a mixture of the product you pose and a bromomethyl benzene through radical halogenation. The question is why the first one is favored. What I can think of so far is that if a bromine radical were to react with a hydrogen in the benzene, then it leaves an extra electron in the already electron-rich ring. Now, remember that the benzene ring is a conjugated system with p-orbitals aligning all parallelly? If you had a residual electron in the conjugated system then you would somewhat distort the conjugated system since the carbon baring that electron would have sp3 like character whereas all other carbons in the ring has sp2. You can also use molecular orbital theory to prove that bromination on the benzene ring is unfavorable. If you had an extra electron in the system, then that electron would be positioned in one of the anti-bonding orbital.
Bromination on the methyl group, on the other hand, would not have much effect on the electronic structure of the molecule since -CH3 is sp3 and that the transition state CH2* is also sp3.
For (b), it's not because of the order of the carbon but because of the reactants you are dealing with. Br2 will "react" with FeBr3 to from an electrophile (Br2FeBr3). Because the benzene can also act as a nucleophile with its double bonds, it will attack one end of the Br (Electrophilic-> Br-BrFeBr3) forming a tetrahedral intermediate carbocation. To restore aromaticity, a base would extract the proton in the same carbon which reforms the bezene ring.
Hope this helps.