What is this part called and where can I find a replacement? Housing assembly? There is no brand on the shower handle...

Looks like a Delta-Delex mixer body. What's wrong with it? The seals in the bottom are replaceable. You may find this at HD, Lowe's or a good plumbing supply store.

The washer deteriorated and I cannot find the type anywhere. I went to home depot and lowe's and they just told me to buy a new shower handle set... I would even do that if I knew what model/brand it is.

The cartridge:
http://farm9.staticflickr.com/8281/7791426796_380b370159.jpg

Where 2 cone/star shaped rubber washers go
http://farm9.staticflickr.com/8438/7791426112_044b9e782d.jpg

Star shaped bottom rubber washer?
http://farm9.staticflickr.com/8300/7791424466_615e9c366a.jpg

Thank you in advance!

The round ones looked like delta type, I could not see they were cone shaped. The star washer I cannot ID. Hopefully some of the very experienced plumbers will see the post and rerspond.