There are several ways to install radiant heating.
You can bury the PEX tubing into a concrete slab.
You can attach the PEX to the bottom of the sub-floor.
The PEX can be stapled to a wood sub-floor and covered with light weight concrete or mortar.
Once the tubing is in place, the finish floor can be installed. Most types of floors can be accommodated but there are design issues to consider with some.
Regular fireplaces are very inefficient. They send most (more than 50%) of their energy up the chimney. The answer is to use a masonry heater. They burn more efficiently and collect more heat during the burn and release it slowly over time. This is how people heat their home in places such as Finland and northern Russia.
Home Technology Group recommends the Tempcast Masonry Heater that is produced in Ontario, Canada.