In media the inflation number that you see is generally the Year-on-Year inflation rate, i.e.,
where $I_t$ is the price index (CPI or WPI). For most countries, the index is a fixed base index. So the absolute value of the index gives you the idea of where the prices are relative to the base year.
Inflation rate on the other hand gives you idea of how much the index has increased as compared to same month previous year. The main reason for using YoY over MoM is to prevent seasonality misleading you.
For example, if media reported MoM, every December you'd see high inflation because of holiday season. So inflation of December is not strictly comparable with other months because of inherent seasonality. To prevent this YoY is used.
On your second point: No inflation does not keep decreasing with time. This would be true if price increases with a decreasing slope. There is no economic reason to believe that.
On third point: if we only looked at inflation rate from a historic point then that number would rather be an increasing number. Then again you would not be able to compare it with previous months' or years' numbers as then the difference of inflation would be of interest.