I can't say about the museum - it was under construction when I visited Philadelphia a few years ago - but the reconstructed Fort Ti is at left center as seen from the summit of Rattlesnake Mountain, in the background below:
One interesting "item" I've heard was displayed there is part or all of George Washington's headquarters marquee (tent). At the beginning of the Revolution in 1775, Washington ordered this huge affair, which consisted of several (3?) separate canvas "structures". I've seen at least two of them, one at the NPS visitor center at Yorktown, and the other I believe at Valley Forge. They survived because Washington's adopted grandson George Washington Parke Custis (father-in-law to Robert E. Lee) stored them at his mansion overlooking Washington on the Potomac. Following his death and the Civil War they were separated, though they belong together as a unit: the smaller one was used by Washington as an inner bed chamber that fit inside the larger one. I don't know which one - or possibly both - is in the museum but I think neither are still at VF or Yorktown.