Did the Mexican Army really destroy the Alamo as they stated they did

For most part yes, Gen. Antonio Lopez de Santa Ana of the Mexican army decimated the little mission of the Alamo killing almost everyone one except one slave named John to tell the story. Little did Santa Ana know that this would be a battle cry to his own demise, "Remember the Alamo." Gen. Sam Houston used it to fuel the fire to take him and his forces down.

They did. Well, depending on specifically what Mexican resource you are using. The only original things that are still standing are the chapel and one of the barracks which is at the modern day Alamo. They have built more walls and added more buildings now but that was not part of the original Alamo

It was rebuild. Now,you can see it in Downtown,San Antonio

It was restored after the battles... parts of it... most of the original fort walls are gone... there also wasn't a roof during the battle, so that is new...

No the alamo still stands