I proposed some change to the monetary system of NXT platform. (if you don't know about it :
http://nxt.org/about/monetary-system/ . It's basically PoW for repartition of coin when PoS secure the network)
It would solve your "second problem". --> Difficulty never go down so no inflation if price is already too low
We need adaptative difficulty and minting cap for mintable currency.
The monetary system is great.
But the mintable part was not part of the plan and so it was added later and I have to say it's very limited and clunky.
Coin are not viable because the difficulty curve is totally linear. You can mint as much coin as you want if you have the hashrate, no competition between minter.
There is absolutely no protection against big surge in hashrate (like ASICS with bitcoin). And ASICS will fataly come one day or the other.
Mintable coin are currently a success in term of activity and fee generated but it will not continue if nothing is done.
To be viable long-term, coin need adaptative difficulty and minting cap !
What is Minting cap : It stop totally the minting once a cap is reached. The minting can continue once at a certain block. For exemple a limit of 10'000 coin / 5000 block
If 10'000 are minted in 2000 blocks, minting is stopped for 3000 blocks
What is Adaptative difficulty : Based on the number of block to reach the limit, difficulty is adjusted proportionally for the next chunk. (like in traditional PoW)
The exeption is : Difficulty only need to increase. If the cap is not reach, difficulty do not need to decrease because minting is not neccesary to coin survival. Monetary system coin still work perfectly if no coin are minted. This way there is no inflation when the cost of mining is superior to the cost of the coin. And that's a huge advantage compared to traditional PoW.