Lightsabers are constructed by every Jedi knight or a Jedi knight may also choose to use his master's lightsaber if the master is in no longer need of it ( like if he is dead) to show his respect for his master.
A lightsaber crystal was a term used to describe any variety of
crystals, gems, stones, or other objects used as the focus in the
construction of a lightsaber.
At the heart of every lightsaber was a set of crystals that resonated
to produce the efficient, powerful blade. While the most common
crystals used in the process were from the Adega system, Ilum, and
Dantooine (in the so-called "Crystal Cave"), Jedi and Sith used a
variety of crystals to produce various colors, effects and unique
abilities. Some crystals could even enhance the Force skills of a
particular user. Other gems, such as colored crystals or diamonds,
were used exclusively for prismatic effects.
Metal was usually chosen to make up the hilt, but a casing carved from
the Brylark tree, wood that is strong as metal, would also work.
The weapon drew power from an appropriately-sized Diatium power cell.
Here You can read here how the ritual of constructing a new lightsaber works.
So to answer your question : No, there aren't a fixed number of lightsabers in the galaxy.
Here is an extract from the summary of the episode in the link:
Ancient Jedi tradition! Six younglings are sent to the secret caverns
of Ilum, where they are tested by The Gathering, an ancient Jedi
ritual where each youngling must harvest a crystal around which they
will construct their own lightsaber.
I hope this answers another part of the question as well: The Jedi gets his lightsaber on successful completion of The Gathering ritual.
Here is a link having the schematic of a lightsaber and stating what powers it.
For more information check this link.
Luke Skywalker meditated on his crystal in Ben Kenobi's home for many days with only R2-D2 to keep him company.
These are my suggestions for your doubts.
Hope this helps.