What are the different uses of 体会? While trying to understand the complete meaning 体会, the examples I found online had many different uses when translated into English. 

体会
to know from experience; to learn through experience; to realize; understanding; experience

请你谈一点个人体会好吗? 
Will you please say a few words about your personal understanding [experience]?
有时候我们也需要生病一下来体会到健康的好处。 
Sometimes we need to be sick to appreciate the blessing of being healthy.
他们体会不到生活的快乐和鼓舞。 
They cannot experience the joy and inspiration of life.
我也是一位母亲，有三个漂亮的女儿，我能体会她的苦楚。 
And, as a mother of three beautiful daughters, I could feel her pain.
我能体会到你的感受。

here it seems as though the most common use is to understand in relationship to what someone else is going through, having been through that ourselves. Is that correct?
体会 connotes that how you feel, what you learn from your experience. In Chinese, 体会有体验和领会的意思. It can be interpreted differently based on the context. 

Take one of your sentences as an example.  


  请你谈一点个人体会好吗; Can you talk a bit about your takeaways (from there)?