Sure, let's correct the errors in each sentence:

1. **When my sister was a child, she would playing with her toy dolls for many hours.**
- Error: B. playing
- Correction: "When my sister was a child, she would play with her toy dolls for many hours."

2. **When my family lived in London, my dad would be a house husband.**
- Error: C. would be
- Correction: "When my family lived in London, my dad was a house husband."

3. **Back then, my uncle would usually stays home and do chores.**
- Error: C. stays
- Correction: "Back then, my uncle would usually stay home and do chores."

4. **When Charlie was a teenager, she would often went climbing on the weekends.**
- Error: C. went
- Correction: "When Charlie was a teenager, she would often go climbing on the weekends."

5. **Tom and Matt would walk 10 km to school when they were students. They always did this.**
- Error: D. did
- Correction: "Tom and Matt would walk 10 km to school when they were students. They always did that."

So, the corrected sentences are:

1. When my sister was a child, she would play with her toy dolls for many hours.
2. When my family lived in London, my dad was a house husband.
3. Back then, my uncle would usually stay home and do chores.
4. When Charlie was a teenager, she would often go climbing on the weekends.
5. Tom and Matt would walk 10 km to school when they were students. They always did that.