Thank you. Do you know if the WH tour also includes the WH Visitor center or shall i book that separately?

Furthermore what is the latest time in a day that a WH tour could be arranged/confirmed?

According to the White House tours website, the tours are generally scheduled between 9:30 am and 12:30 pm, so your afternoons would be open for other activities. (There are no tours given on Sundays or Mondays.) The WH Visitor’s Center is not part of the tour and you can go there on your own anytime during its open hours. You do not need to make an advance booking.

See:

https://www.whitehouse.gov/visit/

https://www.nps.gov/whho/planyourvisit/white-house-visitor-center.htm

As mentioned above, your chances of being able to get a WH tour are slim because there are so many more requests than there are available spaces. But, should you get on a tour, note that it is self-guided—you will not have a tour guide. And only a handful of rooms are open for you to walk through. Having done this tour myself, I would say you can do it in well under 30 minutes, not including the time you spend waiting in line to enter. You may spend more time in the security line than inside the WH.

The public Capitol tour is fine. The guides are well trained and knowledgeable. With a congressional tour, you risk getting a staffer that isn't that good as a guide.

The WH "tour" is actually a misnomer. As Longhorn74 pointed out, it's just a self-guided walk-through of the public areas that you would see on postcards or in a YouTube video. And because flow-through is critical, there aren't a lot of descriptions for people to pause and read.

The Capitol tours are actually well-organized by professional guides. You'll be assigned a set of headphones tuned into your red-jacketed guide who will walk you through the building, narrating along the way. What a Member of Congress could provide are passes that allow you into the House and Senate chambers to see any business that is being conducted that day.

And after the Capitol tour, you can walk across First Street and take in a tour of the Supreme Court building and chambers if there's time!

We thought the public Capitol tour was very good - well worth it and you could book that for later in the day to keep the am open for a possible WH tour. That tour will probably take a little over an hour. After that, get a free timed entry ticket for the Library of Congress (right across the street.) The lobby area is incredibly beautiful and you can see the Gutenberg Bible on display. That can be a fairly quick stop.

We requested tours of the Bureau of Engraving and Printing and White House from our Congressman's office, and got both - but they wound up scheduled 45 minutes apart from each other. I worried about being turned away from the WH tour since we would be late, but decided to try anyway. We had a 9:30 tour scheduled and showed up around 10, and no one said a word. We waited in the security line for much, much longer than we spent inside. As others have said, you see only a small number of rooms. There are guards stationed in them who can answer questions, but no real tour. It's a little underwhelming, TBH. Worth going if you get the tickets, but not a huge miss if you don't.