good idea to use local wallet since we should split our bitcoin to avoid bad things that could happen. is that local wallet like bitcoin core or multibit? i use multibit because its really light to syncronize with the network and its different with bitcoin core which is need too long before its completed syncronize.
Yeah, it's not very wise to keep the coins on the exchanger. They are not ment to be the real wallets and your coins are there at risk. Exchangers are exposed to hackers attacks or your account there could be locked for different reasons. It's good to keep coins on exchangers ony for trading purpose.