Here are the mistakes in each sentence along with the corrections:

1. **Mistake:** "more good"
**Correction:** "better"
**Corrected Sentence:** She can play the piano better than her sister.

2. **Mistake:** "more carefully"
**Correction:** "more careful" (or "carefully than I do")
**Corrected Sentence:** He is more careful than I am.

3. **Mistake:** "very good"
**Correction:** "very well"
**Corrected Sentence:** She cannot speak German very well at the moment.

4. **Mistake:** "hardlier"
**Correction:** "harder"
**Corrected Sentence:** She works harder and gets better results this year.

5. **Mistake:** "much quickly"
**Correction:** "much more quickly"
**Corrected Sentence:** She can read much more quickly now than in the past.

6. **Mistake:** "much bader"
**Correction:** "much worse"
**Corrected Sentence:** My little brother is much worse at maths than me.

7. **Mistake:** "more beautiful"
**Correction:** "more beautifully"
**Corrected Sentence:** She sings more beautifully than her mother does.

8. **Mistake:** "the nicer"
**Correction:** "the nicest"
**Corrected Sentence:** That is the nicest pen in my bag.

9. **Mistake:** "the most easy"
**Correction:** "the easiest"
**Corrected Sentence:** It’s the easiest train today.