The minimum time for PoS is 1 year...
coin age is not affected by whether your wallet is running/unlocked, so no you don't need your 'wallet online on year'. But you should have it on after 365 days in order to be able to mint staked coins. If you don't, it would be like not rolling over a CD in a bank--you could lose compounded interest.
But... I found this gem:
Proof of Stake explanation
20% interest per year if you
3. have wallet online all year
Lol wut?
Ya have wallet online all year? You must be kidding!
Yes, you have, because that way you can an intermediary for transactions.
this is
if you want pos rewards guys, if you dont then dont have it on all year

So the coin's own developer doesn't understand Proof of Stake at all?
are.you.freaking.kidding.me?!?
It is worse than I ever thought...