a) It was flagged it as advanced because it's a configuration that we consider unusual or non-optimal, so we described it as "advanced" in order to discourage it. Leaving the "Display this business process information" checked has no implications other than the fact it would log some additional information about your BP, as BPs do, which I suppose takes some resources, though arguably not much (depending on the BP). This is likely the "performance reason" that is implied here. 

b) For your particular use-case, leaving the option unchecked is probably fine, though some would consider it a non-standard setup for a business process. Disabling the option doesn't really gain you much other than marginal storage and performance gains (though I suppose the usefulness of that would depend on the system and the BP). What you lose from disabling the option is that people who might expect some sort of details on the BP will find none... though it sounds like this isn't particularly relevant to your situation. The logging does keep track of stuff even if you have no BP activities in your workflow. For example, it will record events for the BP being started and for its completion.