i just had blossom end rot on tomatoes. read somewhere that it is caused by lack of calcium. i crumbled eggshells and spread around my plants. they recovered quickly but who knows maybe they would have anyway and the shells weren't significant. just sharing what i read, you can do more research if you are interested...

You can use them pretty much any way you use other summer squashes. They're well-suited to stuffing. Also, I bet they'd be really good in this: http://www.npr.org/2011/07/13/137796299/linguine-with-slow-cooked-zucchini-basil-and-cream

There was a contest last summer for summer squash. Perhaps some of the recipes will interest you. If they are large enough, it would be cool to stuff them.

http://www.food52.com/contests/162

Looks like you have a case of blossom end rot. See info at http://faq.gardenweb.com/faq/lists/tomato/2000082444023571.html

The base of the fruit will be ok, just cut off the brown part...