My bitcoi s was always in secure paper wallets which I can see my private keys. If you are in doubt of what you should do to get you post-fork coins i reccomend for you to store at any wallet which you can control your private keys and withdraw then of all exchanges or hot wallets.
I think during forks bitcoins that are stored on a paper wallet will not be awarded with the new token.
You should put your bitcoins into a wallet that will support the new coin to make sure that you will have it during the fork.
Yes to this.
I use Coinbase + two factor authenticator.
Their announcement about "24hrs" made the deal to me.