[cesarb]

> How does taking out my BTC out of CoinBase ensure I will receive an equivalent amount of BCH?

By taking your BTC out of Coinbase and into a wallet you control directly (on your computer or phone) before the fork, you have the corresponding private keys during the fork, which after the fork can be used to transact the same value independently on both the BTC and BCH chains.

> I bought 200$ worth of BTC in the past from CB, and promptly moved to an Exchange. Does that mean I will get whatever amount of BTC I purchased back then in BCH?

What matters is what happened at the precise moment of the fork. If at that moment your BTC was on an exchange, the corresponding BCH is at that same exchange. What happens with it depends on the exchange: some might treat it as non-existent, some might credit it to you in full (but it might or might not be possible to trade and/or take it out of the exchange), some might credit it to you partially based on a confusing formula which gets changed after the fact, and some might even take all the BCH for themselves.