a) yes, but only if you create such a script
b) It's called a schedule and you use the same part of the admin console that you'd use to schedule a back up of the database to schedule the script to run.
c) Not quite, a database hosted by server is always open. Also you'll need to use an SMTP email server in order to send mail from the server scheduled script, a local email client is not an option for this.
d) if all else fails, it's also possible to use an OS based scheduler to open a FileMaker file on your machine at a specified time each day. This "robot" file can open and connect to the hosted file and perform a script in the hosted file. This script runs as a client of the hosted database and makes it possible to send maile vial an email client instead of an SMTP email server.