During the attorney review period, the property is not officially "under contract". During this period, anything can happen. You can decide to back out for no reason at all. The Seller can accept another offer and cancel your contract. Once attorney review has been completed, then the contract is binding and the listing agent will mark it as "Under Contract" in the MLS.
Please note that Trulia and the other real estate web sites do not always have the most up-to-date information, and still may show the property as available, even after it is under contract. Do not worry about this as the only thing that matters is when it gets out of attorney review, no matter what it says on a website.
1. The listing agent needs to indicate on the MLS that it is under contract.
This will not remove from all websites but will let people know that it is under contract on most sites.
2. Don't worry about it. If you are under contract no one can get in another offer legally
3. There are some homes listed on these site that were never for sale. If you miss a couple of mortgage payments expects it to get posted all over the internet as a possible foreclosure.
Another reason you see the property online is that the listing broker has maintained the property in "active" status. Trulia reports properties that are active for sale.
Your property never stop appearing on real estate web sites. Paying for the property and getting the deed in your name will not remove the property from the real estate information machine we have in this country.