I see a few potential problems.
It looks like your X axis relies on gravity only to hold it down? You'll need to capture the rails top and bottom to keep it from bouncing around. One thing you'll discover is the forces involved are a lot more than you would expect.
1/2" MDF seems a little on the light side. It's pretty flexible. You'll notice most people use 3/4" for on there machines.
Your torsion box table needs to be skinned both top and bottom to be truly rigid. It's the same concept as an I beam just going in two directions. If you removed the bottom flange from an I beam you'd have a T beam, not nearly as rigid.
A 110 cm gantry is pretty wide to be driven by a single lead screw centered under the table. When the router is cutting off to the side the wracking forces will be substantial. Suggest you consider dual screw drives to drive the gantry.
As to the parts you're having trouble sourcing (not sure why McMAsterCarr would refuse to fill an order?)...
Not sure why you need cranks to manually adjust motors. The motors can't be moved at all by hand when the system is under power.
Shaft couplers - do a search for LoveJoy couplers. Pretty easy to find.
Lead nuts - more commonly called anti-backlash nuts. Try DumpsterCNC.com or Roton.com... or McMasterCarr!
Caterpiller track - More commonly called Cable Chain, Cable Carrier or Energy Chain. Manufactured by IGUS. Try, um McMasterCarr(!) or MSC, Grainger or Ebay.
A Dremel seems a little underpowered for use as a spindle on such a big machine, you might consider using a router instead. Lasers are a whole different animal and EXTREMELY DANGEROUS in open machines. Have you ever noticed that all commercial laser cutters are built into enclosures? This is for two reasons. First, the vapors created can be VERY TOXIC and need to be exhausted away and out of the building. Two, if the laser beam reflects off the material and into your eye... well you'll make a good pirate next halloween!