If he bought the buildings, there should be a record of the change of ownership in the Register of Sasines in the National Archives of Scotland
www.nas.gov.uk. You wouldn't need to see the whole document - there should be enough detail in the Abridgment. Calendars of abridgments were published annually, so it means going through them one after the other until you find the transaction. The West Lothian heritage centre or West Lothian archives in Linlithgow may have copies of the calendars and if so might be willing to look them up for you. Otherwise it's a case of hiring a searcher if you can't get to Edinburgh or Linlithgow yourself.
As for the age of the building, you need to find an old photograph of the building. The style of the building will give an indication of its age. Again, the Heritage Centre is probably the best place to start.
Breich Inn is marked and named on the first edition of the Ordnance Survey six-inch map, published in 1854. See
http://maps.nls.uk/os/6inch/view/?sid=74426709#zoom=6&lat=8000&lon=34672&layers=BT