Smart trainer & CX bike compatibility I have a Kona Jake the Snake Frame (2001) and is currently mounted with Continental Gatorskin 700x32c tires and Shimano RS010 622x15c rims. I was hoping to use this on a smart trainer. This setup will be used for software like Rouvy. I'm new to cycling and was hoping someone could help me with some questions:

1.) Is it safe to mount thinner tires on the bike? If so, how thin can I go.

2.) Will the weight of the bike be an issue in choosing a smart trainer?

3.) I'm currently interested in buying a Tacx Bushido since I found a cheap one on chainreactioncycles. On the Tacx website, it says that as long as you use their Tacx 29" trainer tire, you can fit the bike on the trainer. Did I understand this correctly?
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.