Not stupid questions! That you are considering 'cross is great, and it's not hard to do. Watching a race, if you haven't yet, is a good way to see what's going on at first.
A road bike doesn't work so well for 'cross. The main reason is that once you put on the knobby tires (and you will need them - you won't need new wheels though), there won't be enough clearance between the road brakes and the knobby tires. So you'd need to get different brakes - cantilevers or V-brakes, like for mountain bikes.
Once you take care of the tires and the brakes, you could do 'cross on your road bike. That's what they did in the old days. Nowadays, they make bikes that are designed in many ways just for 'cross. The frame angles are more "relaxed" than on a road bike, so the bike is more stable and forgiving. The fork tends to be beefier. People tend to run some easier gearing, and even use a mountain derailleur on the rear.
You'd want to use shoes with lugged soles. Any shoe as long as it's not a smooth-sole road shoe. Clipless pedals are the norm in 'cross racing, but the mountain type, not the road-only type. You could do 'cross on flat pedals, if you had to.
Also, if you have a mountain bike, especially a hard-tail one, you can do 'cross on it. There is no rule in 'cross about what bike to use, as long as there are not bar-ends on the mountain bars. You will almost always see a few people racing 'cross on mountain bikes. It's a good way to see how you like it before getting a 'cross bike. People eventually make the switch, because a 'cross bike is faster than a mountain bike. It has the bigger wheels, skinnier tires, and is lighter.
Don't worry too much about training until you have some races under your belt. You'll figure out what you need to work on. Just figure out how to race 'cross at first.
There may be one to three places on a course where you need to carry your bike. People sometimes make a big deal about the technique for this, but don't worry too much about that, either. You can figure out the technique for it later, and it's not that crucial anyway.
Let us know how you make out!
Sally