I'd be wary of doing a sow and litter class, even with Kunekunes

It's a lot of pigs to keep together, inside a ring and away from other pigs (from a bio-security point of view) plus they'd all have to be tagged, recorded and checked on movement forms and I think it would be a fairly stressful experience for the pig and piglets.
But take along one of your sows or older piglets and have a go

In answer to your questions though,
1) You 'train' the pig to walk with the board (or train yourself to keep up and look like it's trained

) It doesn't always work, sometimes they can get a bit starstruck and stand, rooted to the spot - sometimes they gallop round the ring (and as Mandy & kja say, they sometimes don't even stay in the ring

) but it's all part of the fun of showing pigs

3) The pens I've seen have always been solid sided, but I'm sure someone at whatever show you were planning on going to will be able to tell you for sure, if you're worried about it.
I've trimmed the feet of a very overweight 'micro' pig before (mine tend to wear theirs down in the winter when they're in on concrete

) using heavy duty sheep hoof trimmers. Just take off a little at a time from the front. Make sure their feet are clean and you're only cutting from the hard part (and watch your fingers !) If you get them comatose with a good belly rubbing session (and have someone to continue doing this while you trim) they hardly even notice - if they get super-stressy, just give them a little can of beer

They'll soon be sound aslepp and you can do it then

I've often wondered if the big rasps for doing horses hooves would be any good as a 'nail file' for on-going maintenance - but haven't tried it myself.
Check out the BKKPS website/newsletter for details of shows that have classes for Kunekunes - fingers crossed there will be one close to where you are. Supposing there aren't any classes for Kunes locally, you should still go along and talk to some of the pig keepers - watch them, see how they do it and you'll learn loads

Good luck !