Here are the corrected sentences:

1. **Original**: I want to buy the new table, but the store only has old tables.
**Correction**: I want to buy a new table, but the store only has old tables.

2. **Original**: According to a weather forecast, it is going to rain this week.
**Correction**: According to the weather forecast, it is going to rain this week.

3. **Original**: My brother went to a United State last year.
**Correction**: My brother went to the United States last year.

4. **Original**: Oanh had a hour to do her homework yesterday.
**Correction**: Oanh had an hour to do her homework yesterday.

5. **Original**: Kim didn't have an lot of money to buy a new house for her parents.
**Correction**: Kim didn't have much money to buy a new house for her parents.

6. **Original**: I found a interesting article in the magazine yesterday.
**Correction**: I found an interesting article in the magazine yesterday.

7. **Original**: Your sister is an most intelligent girl I've ever met.
**Correction**: Your sister is the most intelligent girl I've ever met.

8. **Original**: A president of America is Joe Biden now.
**Correction**: The president of America is Joe Biden now.

9. **Original**: I bought a cat in the market yesterday.
**Correction**: I bought a cat at the market yesterday.

10. **Original**: I have the cat. The cat is very nice.
**Correction**: I have a cat. The cat is very nice.

These corrections address grammatical errors and improve clarity in the sentences.