LovesLife, are you saying that you do not believe that homosexuality is a choice? Are you familiar with Ayn Rand's philosophy of Objectivism?
"The law of identity does not permit you to have your cake and eat it, too. The law of causality does not permit you to eat your cake before you have it. . . .
The law of causality is the law of identity applied to action. All actions are caused by entities. The nature of an action is caused and determined by the nature of the entities that act; a thing cannot act in contradiction to its nature."-----Ayn Rand
1. The US should not have had a draft during WWII, or and other war. Instating a military draft is a clear violation of the right to life. As to the second part of this question, I have no response.
2. No, it was not immoral for Ayn Rand to collect Medicare. It is completely okay to accept things like Medicare, so long as you do so as restitution (for being forced to pay for programs you do not approve of), and not as charity, or entitlement to other people's wealth. People living in the US have to pay taxes for programs they may or may not approve of, so it wouldn't be immoral to get some of the money back from the government, provided such money was taken immorally.
3. I don't know quite what you're asking here: is their existence immoral, or is using them immoral? To the first question: public libraries do not involve protecting the rights of citizens, so it is improper for the government to fund them, and they should be private. To the second question: once again, you do pay taxes that support these libraries, so it is okay to use them/benefit from them.
4. I have no good answer for this one, but I know someone else here will.
5. Objectivism is defined as the philosophy of Ayn Rand; therefore, in order for one to be an Objectivist, one must agree with the philosophy of Ayn Rand. Rand was right about philosophical issues. This does not mean, however, that Objectivists believe that Ayn Rand was right about everything or that she was infallible. I'm sure many Objectivists could find something about which they and Rand disagreed. So long as these disagreements are not in contradiction with beliefs that Objectivism explicitly advocates, there's no problem.