[english grammar man]

The correct answers would be:

1. We established a joint venture called Teachers Circle Co. Ltd.
   - The word "there" is not required. Nothing wrong with the word "venture".
2. Next, I'll explain the new curriculum we've developed.
   - The word "about" is not required.
3. I talked with her about my trip to Tasmania.
   - "Island" is not required. Fiji is also a small island, and we DO NOT say "During my holidays I travelled to Fiji island".
4. My wife tried to learn English.
   - Teia: Your sentence is correct, however a slightly different meaning.