When printing out a message or printing out upon recording start, can I print out the date in addition to the time?

Yes. In Basic setting mode, select "Advanced_Function" > "Time_Printout," and then change the printout date and time formats.

You can change the alarm printout, message printout, printout on recording start, and printout on changing of the recording chart speed.

For details, see section 7.16, "Changing the Time Printout Format" in the user's manual.