Here are the corrections for the mistakes in the sentences:

1. **Sally said she will be a teacher someday.**
Correction: **Sally said she would be a teacher someday.**
(In reported speech, "will" is often changed to "would.")

2. **If you feel unwell, you shouldn’t stay in bed.**
No correction needed.

3. **She wanted to know how long did it take to get there.**
Correction: **She wanted to know how long it took to get there.**
(The correct structure is "how long it took," not "how long did it take.")

4. **Why don’t we sharing the cost of accommodation?**
Correction: **Why don’t we share the cost of accommodation?**
(It should be "share" instead of "sharing.")

5. **My home village is on the west of the city.**
No correction needed, but "is in the west of the city" might be more appropriate.

6. **I have passed my driving test six months ago.**
Correction: **I passed my driving test six months ago.**
(Use simple past instead of present perfect for a specific time.)

7. **Are you interesting in learning foreign languages?**
Correction: **Are you interested in learning foreign languages?**
(It should be "interested," not "interesting.")

8. **I’m really looking forward to work with you.**
Correction: **I’m really looking forward to working with you.**
("Looking forward to" is followed by a gerund.)

9. **We arrived at London at 3 o’clock in the morning.**
Correction: **We arrived in London at 3 o’clock in the morning.**
(Use "in London" instead of "at London.")

10. **She told me to shut the door but don’t lock it.**
Correction: **She told me to shut the door but not to lock it.**
(The correct structure is "but not to lock it.")