NO the bidders do NOT really have to qualify except to make a $5,000 deposit in order to bid. The winner can NOT change the historic nature. For example they can NOT paint the lighthouse PINK, because it was never that color. Also, no requirement to start restoring it and of course it becomes private property, the new owner does NOT have to let anyone on.
The history of what I have read, private ownership can be a curse or a blessing. Cape Florida was owned by a private owner who built the sea wall that saved the tower. The family that owned West Rigolets did nothing for 50 years and it washed away (the legs needed repair). So private ownership is a gamble.