All the above...
Particularly, actually take the time to read the shopper's email and understand what it is he or she is asking. Too often, I'll get an email in response to a question, and it's either a canned response or half an answer or it answers a question I didn't ask, but not the question I did ask.
Reply to emails, even if it takes you a day or two. Ignoring emails can be costly to both the scheduler and the shopper.
PICK UP THE PHONE and make a call if you need something from a shopper in a hurry. Some MSCs and their schedulers are very good at that, but it seems there are people who really, really don't want to talk on the phone anymore.
Make sure your shoppers have some way to reach you in an urgent situation. I went around and around with a scheduler and MSC recently because there's literally NO way to get through to anybody. If they don't respond to an email, there's no general phone number, shopper help line, etc., on the website, and no phone number in their schedulers' emails. I get it that they don't want to be bothered with communication that can be handled via email, but if it's an emergency while you're on a shop or you have questions that need to be answered before you do a shop, schedulers need to make sure there's a way to reach them! Seems logical, doesn't it?
I learn something new every day, but not everyday!
I've learned to never trust spell-check or my phone's auto-fill feature.