Question about Palace of Versailles

...the pass does cover my transportation to Palace of Versailles from
Paris and vice versa.

I think you meant to say that it does NOT cover your transport to Versailles.

We followed the RS guide's advice to avoid Tuesdays and went on a Wednesday. It was still extremely crowded when the palace opened in the morning. However, we found that almost no one went out to the gardens. We wished we had planned a full day so that we could explore the vast gardens at our leisure.

You can choose from a variety of tickets at this site https://www.versailles-palace-tickets.com/ but be aware that this is not the official Versailles website. I'm guessing there is a markup on the prices. Still, the information about the entry options is useful (refer to the map of Entrance A and Entrance B on the web page):
"If you have not purchased your tickets online, you will have to stand in queue at the ticket counter before entering via Entrance A. While the wait times at the ticket counter can take anything between 15 to 30 minutes the security check at Entrance A circles around 30 minutes to 2 hours.
If you have purchased a general admission ticket online, you can enter via Entrance A. The wait in queue here can be anywhere from 30 minutes to 2 hours.
If you have purchased skip the line tickets or tickets for a guided tour online, you can enter via Entrance B. This entrance is the quickest way to access the Palace with hardly any wait time."

We purchased a guided tour ("Visite Guidee") but we didn't realize how crowded it would be inside of Entrance A, so we had quite a time getting out so that we could run across the courtyard to Entrance B to begin our tour at the appointed hour. The guided tour was excellent and I would recommend that as the best value. Once the guided tour is over, you are already inside the palace and you have access to the same rooms as the general public, as well as being free to go out into the gardens and explore the other structures (Grand Trianon, Hameau, etc.).

The official Versailles website is here http://en.chateauversailles.fr/plan-your-visit/practical-information Note the cautions about changes in opening hours due to anti-terrorism efforts.

Hope this helps!

MathRobot, be aware that the pass does not cover entrance to the gardens during Musical Gardens, Musical Fountains or other special shows: they are an additional price. And please don't use anything but the OFFICIAL website for the chateau.

http://en.chateauversailles.fr

Text regarding the garden shows:
http://en.chateauversailles.fr/plan-your-visit/conditions-free-admission#reduced-rates

The Paris Museum Pass grants admission to the Palace of Versailles,
the palaces of Trianon and more than 60 museums and monuments in Paris
and the Paris region. It does not grant admission to the Gardens on
Musical Fountains show and Musical Gardens

Days that Musical Fountains and Musical Gardens are held:
http://en.chateauversailles.fr/news/shows/fountains-shows-and-musical-gardens

To repeat Janet's previous advice from your related thread:

The pass gives zero priority at Versailles. I would try to do that on
a day the pass didn't cover and buy a timed entry rather than stand
for two hours in the sun in the security line. Or get a Kings
Apartment Tour which then leaves you in the chateau.

If you must do Versailles on the PMP then arrive about an hour before it opens i.e. get to perimeter security at 8 and you should be close enough to the front of the line for it to not take much more than the hour to get in. If it is sunny bring an umbrella for standing in sun in the line or at least wear a good sun hat.

Or do the King's apartment Tour -- when you arrive for that you get to wait in an air conditioned waiting room with rest rooms and padded benches until the time of the tour.

Q1: When should we arrive to the Palace of Versailles in order to avoid waiting for the huge line ups? What days of the week should we go? Which days in the week are the busiest?

-I've heard you want to avoid Tuesdays and weekends because those are the busiest days. From another post I gather you'll be doing this in August, so don't forget hats, umbrellas, sunscreen.

-There are three schools of thought for timing your visit - arrive early and wait in line before it opens, arrive late hoping there won't be much of a line, or pre-book a tour of the Kings Apartments.

Q2: How many hours should we spend on the Palace of Versailles? Should we spend a whole day there?

• I spent the whole day: a few hours inside the Palace and the rest touring the grounds, Grand Trianon, and Hameau. Look at the write up in a guidebook and see if that sounds interesting to you. It's a lot of walking and I was there in April.

Q3: What places you recommend we see or do in Palace of Versailles?

-Inside the Palace/Chateau there's a pre-determined route you follow with the famous Hall of Mirrors about three-quarters of the way through and a gift shop at the end.