Slew rate (SR) is the maximum rate of change (slope) of the output voltage. For instance, a specification of 5 V/μs means that in 1 μs, the maximum rate of output change cannot be more than ±5V.
In an op-amp datasheet, the slew rate is typically expressed in the terms of V/μs and it tells you how fast the output of the op-amp can follow its input.
Refer to the voltage follower below, when given a stop input from 0V to 5V, see what happened at the output.
Rising time usually refers to the time it takes for a voltage to rise from 10% to 90% of its peak value.
Falling time usually refers to the time it takes for a voltage to rise from 90% to 10% of its peak value.