You can enabled/disable the property for visibility of each plot (see attach vi).
Concerning the time issue, I had the same problem a a few years back when I start using labview, and I forgot how I fixed it. It seem that one would want to access the property "scaling factor : xo" and set it to the time/date the vi start. I am unfortunatly unable to find that property (in property node). Hopefully someone else will find the answer for that part of your question.
Regards
Philippe Guerit