in general most of the off-roading in a cross race will be as you say, on grass, dirt/mud paths. however, in some smaller, local races you may very well encounter "jungle cross" terrain, which could range from singletrack, mtb-type trails to rocky run ups, log barriers, roots, rocks, etc. but, at least in my experience, even then the terrain isn't TOO crazy. that is, i've never encountered big rock gardens or super gnarly stuff on a cross course.
as for sand, that also depends on the course. many courses will have a short section that is made up of very loose beach-type sand. personally, i have never seen really loose gravel on cross a race course. how you get thru the sand is a matter of preference. some ppl will ride it, and some ppl will run it, even if its totally flat. it really depends on your momentum and whether or not you feel comfortable pedaling and steering your way thru it. i tend to run the sandy sections because i think i'm faster on my feet going thru it than trying to spin my way thru it (and getting really tired in the process).
as for wheels and tire pressure, this, like in every other discipline of cycling, can be as scientific (or as simple) as you want it to be. most of the pros will run tubulars because they are lighter than clinchers and you can run much lower tire pressures with them without the risk of getting a flat. its nice to be able to run low pressure on a cross course because this will give you much more traction on the all of the varied terrain. its just the opposite from a road race, where your tires might be super hard. in cross, its the perfect low pressure that racers are looking for. having said that, every course is different and, depending on the weather, etc., you will have to adjust accordingly. this is a good reason why its always a good idea to pre-ride the course a few times b4 the race -- get a feel for the terrain and adjust your pressure to suit it.
as for training, i never practice for cross on "extreme" terrain. most of the training i do is on the road, or on a grassy/dirt circuit. however, taking your cross bike on mtb trails is a good idea because it will teach you good handling skills, and its FUN. i do this more as a "break" from training as opposed to something i do on a regular basis.
the most important thing with regard to cross racing is your engine. you have to be able to hammer at a very high intensity the entire time...so interval training is also a big part of my training regimen.