Coin days is not flawed. If you have 100 coins and let them age for 10 days, you have ten times as much stake as someone who has 10 coins and let them age for 10 days. Compare apple to apples, not oranges.
1. Then people can just keep reusing stake.
2. Cryptocurrencies needs to be decentralized. You can't identify who one "miner" is.
3. See 2.
Completely agree. I think stake should be linearly related to coin amount, and less than linearly related to age. EG: Stake = coins*(1-e^-(age in days))
That's an interesting variation. However, the formula could use a little tweaking. After only 10 days, your coins have already attained 99.99546% of their stake. This system then is not very different than my suggestion #1, just using the amount of coins as the measurement of stake. However, I think my suggested system #3 is stronger. It is something like Meni's Implementation of a Proof of Stake system (
https://en.bitcoin.it/wiki/Proof_of_Stake#Meni.27s_implementation).