yes and no, in regards to holding and not selling. and yes, it does need to be held in. a certain place to qualify (for a period of time).
in order to delegate your ADA, it currently needs to be in a cold wallet that supports delegating. at the moment as far as i can tell there are only two wallets that do (Daedalus and Yoroi)
delegating doesn’t just mean having your ada in the wallet, you have to explicitly go to the delegation centre, select a stake pool then select the option to delegate to that pool of your choice. once you’ve done that, and an epoch has begun, technically at this point you can move, sell and do whatever you want with your ADA without it affecting the rewards that you’re owed - for delegating when the epoch begun - come the end of the epoch. and these rewards will go into the same wallet.
now come the next epoch, (if you’d sold or something after the previous epoch had begun, or maybe the opposite, you’d bought more) you’re only going to get the amount of rewards proportional to how much was in the wallet at the start of this new epoch.
for reference you can think of epochs and slots, like pages and lines. each epoch has a number of slots contained within it, the same way a page has a number of lines contained within it, or a paragraph contains sentences. and each epoch is approximately ~ 5 days long.
at some point in the future, yes, that might be the case BUT for the moment - no, not it does not.
how staking-as-a-service might apply for Ada held on exchanges has as of now not yet been disclosed. but it might be possible in the near future as it’s been/being worked on. in the mean time, please never leave your funds on exchanges, it’s not good practice. move them to a cold 
wallet which you control, meaning one which you have the keys to.
there’s an important distinction to make here however, crypto.com offer two services which could very easily be conflate/confused. they have an app and a wallet (recently released).
while they both are technically apps and both have wallets, the distinction is one, what they refer to as “App”, is what is what is known as a hot 
wallet (you’re not in control of your keys, and as a consequence you’re not in control of your funds = not good 
). while the other, what they call “wallet” is what is know as a cold wallet (you’re in control of your keys, and as a consequence you’re in control of your funds = very good 
).