Is it OK for me to use ideas from someone else's answer in mine? For example, if I post an answer, and someone else posts an answer or comment with an additional idea, can I incorporate their idea into my answer?
Yes, if it complements or completes your answer (so it's not just a rip-off but really an organic addition to what you are saying). Make sure you give them credit for the idea. I tend to do something like
A general way to achieve this is xyz. (Or, as @username says, you could do abc.)
It's important to remember that one of the main ideas behind Stack Overflow is that it becomes a general repository of quality questions and answers. This is the reasoning behind a lot of how the site is designed, from being able to edit (almost) anybody’s posts to community moderation. As such it is entirely OK, and I would say even encouraged to include information from someone else.
In short as @probably Pekka says yes as long as it an organic addition to what your saying and you make sure to credit them...