Rewrite as indicated below. The first is already done as an example.
1. Pam was not felling well, however she went to school.
=> Although Pam was not feeling well, she went to school.
=> In spite of not feeling well, Pam went to school.
2. Tom was seriously advised by his teacher, but he insisted in disturbing the class.
a. Although Tom was seriously advised by his teacher, he insisted in disturbing the class.
b. In spite of the fact that Tom was seriously advised by his teacher,he insisted in disturbing the class.
3. Mary tried several times, but she couldn't find a taxi.
a. Although Mary tried several times, she couldn't find a taxi.
b. In spite of trying several times, Mary couldn't find a taxi.
4. Although he felt tired, he stayed up to keeps us company.
=> Despite feeling tired, he stayed up to keeps us company.
5. They didn't have much time, however they came to visit us.
=> In spite of not having much time, they came to visit us.
6. He is too old, but he still does his gymnastics every morning.
a. Although he is too old, he still does his gymnastics every morning.
b. Despite being too old, he still does his gymnastics every morning.
7. Although the shirts are very expensive, people buy them because they are trendy.
=> In spite of the expensive shirts, people buy them because they are trendy.
8. Although he had no qualification for it, he got the job.
=> In spite of having no qualification for it, he got the job.
9. I didn't like the CD you have recommended me, but I bought it all the same.
a. Although I didn't like the CD you have recommended me, I bought it all the same.
b. In spite of that fact that I didn't like the CD you have recommended me, I bought it all the same.
10. I told her all the truth. However she didn't believe me.
a. Although I told her all the truth, she didn't believe me.
b. In spite of the fact that I told her all the truth, she didn't believe me.