Hi, well yours is a common question so you'll find some threads covering this type of conversion in the archives.
I actually started with a CNC router and added a laser but quickly found the solution was not ideal. Of course I wanted to keep the router function too. It actually works ok (not great) with a diode laser but not a CO2 tube.
The CO2 tube will work at any angle, no problem there but it's fragile so best mounted in a fixed position. If you have a water cooled or flowing gas laser then I would definately go with a fixed installation.
The other problem is that a router XY table is designed to have the torque necessary to carry a load (the Z-axis and spindle) and drive the cutter into a material (causing some side load). This usually means lead/ball screws and heavier motors, which in turn have lower acceleration and reduced top speed. A flying optics laser on the other hand is light (only a small mirror / lens assembly is required on the head) so benefits from a lighter setup using belt drive and high speed low inertia motors etc. If raster engraving this is even more important but for cutting you'll also find the router table restricts your maximum power output.
If the mirrors are clean, they should not get hot but any fumes or particles on the mirror will generate heat and potentially crack or damage the mirror. The same is true of the lens which is why most systems use air to shield the mirrors and lens from fumes. The need for such a system depends on what you intend to cut. Air assist is also a requirement for most cutting, where the air comes from a cone mounted to the bottom of the focus lens and helps remove the vapourized gases from the cut path (to prevent restriction of the laser which results in a deeper and cleaner cut).