Short answers, pulled from the story.
Robert Ascher published the first paper on experimental archaeology in 1961 within American Anthropologist. This work established a framework for testing archaeological hypotheses through replication rather than speculation.
Butser Ancient Farm opened its gates in Hampshire, UK, during the early 1970s to recreate buildings from local archaeology. The site now features a working Stone Age farm alongside Bronze Age roundhouses and Iron Age villages.
Thor Heyerdahl sailed a balsa raft named Kon-Tiki from Peru to Polynesia in 1947 to demonstrate cultural exchange possibilities. Modern researchers have attempted to transport large stones similar to those used in Stonehenge using only technology available at the time.
University College Dublin founded its Centre for Experimental Archaeology and Material Culture in 2012 as one of only two such facilities globally. This center conducts research on Mesolithic houses, pottery, bronze working, and food production.
The 1978 BBC TV series Living in the Past re-created life in an Iron Age village using fifteen volunteers over thirteen months. Discovery Channel's MythBusters often conduct experimental archaeology to test capabilities of mythical ancient weapons like Archimedes' death ray.