Can you reuse a Daedalus wallet address saved on an exchange?
Yes - you can. Using new addresses is for your privacy (so that your history isnt *easily visible ), but you can reuse address, yes
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Starting with Shelley staking addresses, not private. If you see one address of the wallet you can look them all up. They are linked by the staking component in the 2nd half of the addresses. It is how the protocol knows the total of your wallet for staking.
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Yip - indeed, that’s true for stake addresses 
Also, protocol expect 80% of the participants to stake, so the rest 20% is available for those who choose privacy over staking, but that would require Daedalus to support the multi account feature, which is currently not. Also, this would be hard to achieve on HW wallets as they do not support multi account. One possible solution is use some standard of a high index range for those semi privacy (pure payment) addresses. Or two different Cardano app on ledger, one for staking and one for not.