Does for staking wallet must be online all time?
closing it wont do any harm. the stake age will build up but it is better to leave it open as often as possible as it supports the transactions on the network (this will be more important when POW stage ends)
Yes you are rewarded stake for maintaining the network by keeping your wallet open and unlocked.
So now I have to opposite information. Which one is true?
And second question about staking: how much I can earn with staking. Suppose I have 100 SLG in coin: until now first staking reaward was bigest one, second was about half of first, and third one is half of second reward or 1/4 of first reward. All three are tiny pieces of one SLG.
So if I buy 1000 SLG and put in wallet make it open and staking, when will I earn lets say 1 SLG?