Dear Madita,
Are you able to read the WHO_AM_I register (0x0C). This is the first thing I would recommend to check before initialization of the device.
You should see something like this:

1. Send a start sequence
2. Send 0x40 // FXAS21002 slave address with the R/W bit low or 0x20 << 1
3. Send 0x0C
4. Send a start sequence again (repeated start)
5. Send 0x41 // FXAS21002 slave address with the R/W bit high or (0x20 << 1) | 0x01
6. Read the data byte from WHO_AM_I register
7. Send NAK and the stop sequence
A common problem during the read operation is that some customers send the stop condition (a LOW to HIGH transition of SDA while SCL is HIGH) instead of sending the repeated start condition after the second byte (0x0C), so please double check it.
Since you have an oscilloscope, can you please post here a plot illustrating what is going on on the bus when you read the WHO_AM_I register? Also a picture illustrating the traffic when writing to the CTRL_REG1 register might be helpful.
Best regards,
Tomas
PS: If my answer helps to solve your question, please mark it as "Correct" or “Helpful”. Thank you.