Do I need to drain the reservoir before swapping the old pump out?

Draining is not required, but it makes the job cleaner. If you leave fluid in, just work carefully to avoid spills when you disconnect the hoses and pull the old pump free.

Will this pump work if my washer fluid line is cracked or kinked?

A new pump can't overcome a damaged line. Check your hoses for splits or pinches while you have the pump out — replace any bad sections so the new pump can do its job.

What if the pump runs but no fluid comes out?

Air in the line is the usual culprit after installation. Activate the washer spray several times to purge air, then let it sit for a minute and try again. Fluid should flow steadily after that.