Preserving artifacts and limited museum access? (Versailles, etc) Career/process questions

Answers to these questions vary widely. I've never been to Versailles, so I have no idea why Versailles in particular limits access; however, I can give you some general answers to your questions based on other historic sites.

First of all, access to "off-limits" location, objects in storage etc., usually comes with a legitimate research interest in those places. If you were a researcher of royal religious sites or something, you could ask for permission to view the royal chapel and Versailles for your research.

Telling what is authentic in a historic site? Ask a guide! They should be able to describe what is original. Most historic sites are a combination of original, period (as in, accurate to the period, but purchased from another site to fill a room), or recreations. But what exactly is "original"? Original to when the house was built? When it was last occupied? Some other period (e.g. a famous occupant?) Historic sites make careful choices about how to present their sites, including what to do about modern renovations. For example, most historic sites have been wired with electricity and central heating either as part of their history or to accommodate visitors safely. If a site is staged to look like sometime in the mid-18th century, it may have been retrofitted with candelabras "similar to" those that were removed a century ago.

Typically soft furnishings (carpets, upholstery, curtains) and wallpaper are not original, simply because they do not last very long (fading, peeling, moths, the bums of a hundred years etc). Often, what you're seeing on the walls is a replica wall-covering designed to look similar to what the building would have had. Sometimes, this is an actual replica of wallpaper discovered during renovation. Sometimes, a house may even leave a patch of original wall-covering, so you can see what it looked like prior to restoration. You may be seeing old flooring if you notice that other carpets have been laid over the top of the existing ones, but how hold is a question a guide could answer. Ask them!

As for why certain locations in a historic site may be off limits, here's some reasons I've encountered:

Renovation/repairs.
The house is occupied and the residents don't want you looking at their modern bedroom.
Preservation/anti-theft (delicate/expensive contents; perhaps rooms are only available to view on guided tours).
Offices. This is a big one. Most historic buildings have on-site offices to look after the hordes of tourists. Where are those offices? In the rooms of the house. Go through a door and you find the lunchroom for the guides, or the security office. Unromantic, I know. (No, actually it's amazing. I volunteered one summer at a site and walking between tourist areas and non-tourist lunchrooms and offices and research areas and the security office was like having superpowers. )
Other rooms that have another life: perhaps they provide programming for schools, host weddings/events, or, in the case of some historic sites, research/preservation work.

If you're interested in standing historic sites, you may want to consider doing a museum or history degree in lieu of an archaeology degree. There are overlaps, of course, but sounds like you're interested in some kind of history: the history of architecture, design, home life ec. would put you in the right place. From the actual perspective or curating, restoring. preserving or running these sites, that would be a museum-type degree.