This would also depend on the anonymity set. If many shares have the same reward, they should be indistinguishable. One could argue that the whole point about accounting is to delay withdrawals, so it's harder and harder for the mint to correlate your payments.
To your second point: this was just very recently proposed and we are going to add an expiry date to each keyset so that wallets know when to rotate out into a new keyset or withdraw from the mint at an announced date.