Trees, especially old trees, will shed some branches due to stress or shading or other biotic or abiotic factors. Dead limbs should be removed using good pruning techniques. 
In order to give you the best response to the last part of the  question, the tree needs to be looked at by a professional. Your local Cooperative Extension Service office is a good place to start. 
For contact info, click here: http://extension.ca.uky.edu/county