I suggest that you always put every service request in writing (email or letter) to the manager, so you have proof that you requested it. In my opinion, you are asking for reasonable requests (pest control for the roaches, working heat which is required , and a glass repair that the managers vendor broke).
If you submit these requests in writing along with your November rent and they cash the rent, they cannot say the requests were not received. As you probably know, just because a manager would like you to move that doesn't mean that you have to move. It is always best to try to work things out amicably before involving the city. If all of your requests go unanswered, you can ask LAHD to step in and require the owner to handle them.
I hope you can avoid that with clear and direct communication.