Gerund or Infinitive??

Hi,

I was having a lot of problems identifying infitives and gerunds so I've spent a while looking up some basic rules and advice. I have been trying to to identify whether the highlighted words are gerunds or infinitives in the following sentences. There are some that I am 99% sure are correct, but there are still quite a few that I'm not too sure about. I would really appreciate it if someone would look over the following sentences and my answers to see if they are correct, or if I need to keep on researching!

1. I began teaching my class last September. GERUND
2. I can't be bothered to do my homework. INFINITIVE
3. I can't bear watching my brother climb without ropes. GERUND
4. I must stop saying "okay" all the time. GERUND
5. I must begin teaching at once. GERUND
6. I enjoy watching movies. GERUND
7. I hate to see people suffer. INFINITIVE
8. I insist on seeing her immediately. GERUND
9. I intend to finish my work by the end of the day. INFINITIVE
10. I like to swim in the sea. INFINITIVE
11. I love eating out. GERUND
12. I dislike looking at violence on TV. GERUND
13. I would prefer to eat out tonight. INFINITIVE
14. Charles proposes dining at The Cheesecake Factory. GERUND
15. I started to feel ill after eating so much rich food. INFINITIVE

Thank you!

Katie