Here are the corrections for the sentences provided:

1. **Mistake**: "love"
**Correction**: "loves"
**Corrected Sentence**: My mother loves eating traditional dishes but she likes local restaurants.

2. **Mistake**: "goes to only one place"
**Correction**: "only goes to one place"
**Corrected Sentence**: There are many hairdressers in my hometown, so my teacher only goes to one place to cut her hair.

3. **Mistake**: "and" (not a mistake, but a suggestion for rephrasing for clarity)
**Correction**: "or"
**Corrected Sentence**: Stop smoking or you will suffer from lung cancer.

4. **Mistake**: "for a date"
**Correction**: "to meet them." (for clarity)
**Corrected Sentence**: I want to meet my friends, so I call them to meet them.

5. **Mistake**: "so they are always overcrowded."
**Correction**: "but they are always overcrowded."
**Corrected Sentence**: There are numerous big and modern hospitals in the city, but they are always overcrowded.

6. **Mistake**: "homework before 5 pm and my mother won’t let me"
**Correction**: "before 5 pm, and my mother won't let me"
**Corrected Sentence**: I need to finish my homework before 5 pm, and my mother won't let me hang out with friends.

7. **Mistake**: "drinking ice water"
**Correction**: "drinking too much ice water" (to clarify)
**Corrected Sentence**: My brother has to stop drinking too much ice water so he will have some throat.

8. **Mistake**: "and I still think"
**Correction**: "but I still think"
**Corrected Sentence**: It is hard to win this contest, but I still think my daughter will be the champion.

9. **Mistake**: "I like drinking beer."
**Correction**: "rather than drinking beer."
**Corrected Sentence**: I have to admit that I love eating fast food rather than drinking beer.

Feel free to ask if you need further assistance!