Can anybody explain me, if I own a piece of art that is worth $1,000,000 USD. After I  tokenize it, what happens to the physical piece of art? Do I keep the physical item or send it to a designated location?

Check white paper page 16

Dear supporters! Don't forget that you can get 12% for purchasing right now 😊  This offer is available for 1,7m tokens only!

Currently the total value is not big.
The platform is operational. Our early adopters are actively trading & giving feedback.  We are finalizing legal issues & polishing the process..
LAToken Team also understands we need more clarity and transparency for our clients. We'll do it right after the Token Sale & make announcements.

What are the known latoken strategic partners?

Security - Rivetz International, Assets - My Gold and Slim Ventures, Legal - DLA Piper
You can read more about strategic partners in our white paper

At times less than in fiat world 

Great! And transaction fees for trading?

And what about appraisal, insurance, trustee fees?