Today on Start Screen when I open New Project, some project templates are missing, expecially the default project that I used.

Did you update to CbB from SPlat? Because it won't see your old templates from SPlat. 
 
If that's the case, move your templates from the SPlat Project Templates folder to the Cakewalk Core Project Templates folder.
 
Also, every time you update CbB it will overwrite the Basic* template. If this is the case, just setup the Project the way you want it, 'Save As' Template and name it something else besides Basic.
 
There was a way to choose which Project Template was the default, but I forgot how to do that or even if it can be done in CbB

[SOLVED]
I've found in some folder the CbB icon of my previous default Project template (AD2 map). Copied and pasted on desktop. Opened CdB start screen new project window and copied and pasted  from desktop the AD2 map icon.
After that it was easy to make that my default project template.
 

Glad you got it working the way you need it.