Well, if you don't have a lot of money, it can be pretty expensive. Your first race, you need to buy an AMA card ($40), a district card (probably $15-$20), pay the gate fee ($5-$10) and the entry fee ($20-$30). Plus, obviously fuel and oil for the bike, gasoline for your haul vehicle and food for you. So, all said and done, your first race might set you back $120-$150 total. After that, it will get cheaper, though, because you'll have the AMA and district card.
As for getting slammed into a tree, you very well might, but that's the risk of racing in the woods. You'll probably be OK, though. The first rule to remember is when the A and AA guys lap you to get out of the way -- not getting out of their way is a sure-fire way to get slammed into a tree, and hard.
As for doing well, don't even worry about that. Most people don't ride at full race speed for two hours without any breaks, which is what a harescramble is, so you really don't know how your body will handle it. You might do great in your first harescramble, you might bonk. Who knows? Who cares? Just ride within your abilities and have fun.
Want to have an even better time? You had a couple bikes listed above your post. Suggest to your dad he race the old bike in the +40 or +30 class and you race yours in C or Trailrider, whatever they call it over there.
A cheaper alternative for you guys might be a local club race. I obviously have no idea if you have these over there, but we have some in our neck of the woods. Basically, they are of shorter duration on shorter courses and aren't sanctioned by the AMA. You also get less serious participants, so they're a lot safer. They are far cheaper both in terms of not needing any memberships and lower entry fees. Personally, unless I was strapped for cash that week, I wouldn't get into the little club races so much, but for someone who has never done a harescramble before, regardless of that person's skill level, I'd definitely suggest them.
However you go about it, certainly go for it. Harescrambles are an absolute blast.