What is the best regression analysis for determining relationship between improvement in HbA1c and education, gender and improvement in drug adherence and diabetes self-management.

Knowing that most of the improvement values are not normally distributed

so,

1. Can I convert abnormally distributed data using Log transformation, then go with regression analysis?

2. Which test is the best? linear regression or multiple linear regeression in my case (after log transformation)

3. In log transformation do I need to transfer all data (the normally and abnormally distributed) to ensure consistency, or just transform the abnormal ones and put other data as it is and do regression?