Q.Guava tree disease
We are renting a house and there was a mature guava tree when we moved in. When the tree bore fruit, all the fruit seemed rotten. It was hard to tell if it was mushy rotten or bug rotten. I tried picking the fruit green, but no matter how I let it ripen (on the tree, off the tree), it was rotten when ripe. What disease or pest might this be? What can I do to address it?

There are several known diseases of the Guava Tree fruit that can cause the rotting of fruit.
Here are some links that I found that will help you understand the issue.
https://www.gardeningknowhow.com/edible/fruits/guava/growing-guava-fruit-trees.htm
http://www.ncbi.nlm.nih.gov/pubmed/754575
http://www.extento.hawaii.edu/kbase/crop/crops/i_guava.htm