Rents are only a part of inflation measurements and can easily outpace the general rate.

California's recent rent control laws caps rent increases at 10% or 5% + the yearly CPI increase (whichever is less) every year, for example, explicitly allowing rent increases to outpace the general inflation rate. Personally, the rent I pay has gone up 9% this year.

Rents can change based on whether an area becomes more or less desirable, as insurance or other costs for landlords change, as ownership of rental units consolidates, etc.--that is, for many reasons that might be only tangentially connected or even completely divorced from the reasons that the costs of other goods and services are changing.

No, rents go up and down for reasons other than inflation.

That is another type of inflation, but it's an interesting point that you may care about both the general consumer inflation rate (for its interaction with the mortgage interest rate) and the rent price inflation rate.

I just assumed the inflation rate was applied to both rent and house price, as a general change in the value of a dollar. While they mostly move in line together, rent prices and home prices don't always move together so a change in value term that effects one and not the other might be useful.