What is a reasonable time to evaluate an offer? - Reasonable should be spelled out by the offeror. I've seen offers with no time limit, and I've seen 72 hour offers. It depends.
What if an offer comes after a camp or showcase but without an "official" visit? Is it reasonable to request an official visit? - It is more than reasonable to request an official or unofficial visit depending on the date, time line, and availability of official visit slots. Unofficial visits are more likely since most offers happen before the NCAA imposed official visit dates.
What is the role of parent here? Should all contact be through HS/Club coach and son or is it appropriate for me to want to meet the coach and ask questions about the program myself directly before accepting an offer - Honestly, I think the parent becomes the "backseat voice of reason". I listened to my son make his business case for his selection among some really good schools. Since some of it was family money with two younger brothers behind him, I wanted to be sure it was the best choice based on his logic and reasoning. I also wanted to be sure he would be able to pay off his student loan in a short period of time. It is appropriate for the parent to meet with Financial Aid and/or to talk to the Coach about scholarship dollars. Let your son handle everything else baseball related, because in a few months he will be doing exactly that.
JMO, and good luck!