I have a Bitcoin wallet through an exchange, can I have a wallet not attached to an exchange? or multiple wallets? if the exchange has problems = I have problems 
For online wallet i recomend you to use blockchain.info and i recomend to use imported wallet for multiple signature because blockchain.info now only can use multiple sign by imported addres, you can create your own wallet by bitaddres.org and import that to your blockchain.
For offline wallet i recomend bitcoin core i use that but you really need big harddisk space.