Can I use a prepaid travel card (loaded with South African Rand) to purchase attraction tickets online?

I'm assuming you're referring to "MasterCard Everyday Prepaid Cards".

From MasterCard's official website:

You can use your MasterCard Everyday Prepaid Card anywhere Debit MasterCard cards are accepted—that's millions of locations worldwide from retail stores to online, mail, and phone orders. You can also use your card to pay bills online.

So, as long as an establishment accepts MasterCard debit cards, it will also accept "MasterCard Everyday Prepaid Cards".

While the source doesn't say it explicitly, the specific mention of "debit cards" may suggest that some establishments may only accept credit cards (and not debit cards.) The implication seems to be that these establishments (if they exist) may not support prepaid cards either. That's something I would check with each establishment.

However, I very much doubt that this would be a problem. These days, almost anyone who accepts credit cards accepts debit cards too. Also:

Credit cards and cash:

All major credit cards can be used in South Africa, with American Express and Diners Club enjoying less universal acceptance than MasterCard and Visa. If you have a so-called "chip card", you will be required to enter a pin code. Pin-based debit cards are often accepted too. Remember to notify your bank in advance that you will be travelling.

According to the first source, the "MasterCard Everyday Prepaid Cards" will play exactly like normal MasterCard debit cards.

^{The emphasis is mine in both quotes.}

For a MasterCard (or Visa, or AmEx, etc.) branded card, so long as there are sufficient funds in the account when the authorization is done, yes. It behaves just like any other Credit or Debit card.

Also, the currency in the account is not so much an issue. The hold and settlement will be done at the prevailing rate.