Smart trainer & CX bike compatibility
I will try to answer as best i can without going into too much detail,

1 : With a 15c rim you can mount 23, 25, 28 and 32 tires Sheldon brown Tire Sizing

2 : Bike weight, Tacx don't specifically list any info regarding bike weight, as the user of the bike on the trainer can vary, I doubt this will be issue unless we're talking excessive weight.

3 : Tacx recommend the use of their tire as it has been designed to run without overheating, a quick search on the Tacx website has the 4 different sizes listed for 40 euros (Doesn't sound to bad to be fair) Tacx Tires

Hopefully this helps you out.