Yes, most limes are insoluble and this will help it to reach the soil and root zone more quickly
I use a newer generation of enhanced lime that breaks down and adjusts the soil pH more quickly. An organic acid is added to limestone to make the lime readily available. This lime can do in months what would take two years for traditional lime to work.
No. However, lime adjusts the soil’s pH so that moss has less favorable growing conditions.
You can apply lime any time in the spring and fall for the most effective retention.