The main component is the relation to the Heroic Spirit.
No one other than Shirou really projects from "thin air"
You usually have a basis/template, and you project your thing over it.
Also if it's a sword Shirou's projections would have the history behind it. So like you could use inno durandal as a catalyst or whatever.
As per the example of the round table. It is possible to project the round table. However, it would take as much trouble as actually getting a round table.
And the round table's core is like Galahad's shield so that's bad example anyway.
Anyway, for Magus A-okay to project the round table they would need the blueprints to the Round Table and they would also need a table that is close to the Round table.
Like how Rin wanted Shirou to use the Azoth and project the Jewel Sword over it. And she plugged all her remaining A rank jewels into the Azoth as well. That's like 1/2 10 years worth of Rin magical energy.
Either way, projecting a catalyst is possible but as long as the catalyst is something that actually exists, it's probably easier to just get the catalyst.
Projection is useful for making something that no longer exists but you need it.