So, even if we know this address is bogus and I have the transaction info from my wallet that I sent it from the coins can not be recovered?
Unless you have the private key cached in your borwser, no it can't be recovered.
It seems like that means there will be 17 BC just sitting randomly in an address that belongs to no one.
This is exactly what it means.
Why can this not be recovered, especially if I know it was supposed to be my address?
Because nobody has the private key for the address.
I don't think my browser was saving any history. I'm guessing I will not be able to recover this downloadable "backup"?
Did you try? "guessing" that you will not be able to recover this downloadable "backup" sounds like a good way to lose the coins for sure.
Why would blockchain show an address when it is not synced and not let the user(especially if they are new and unfamiliar with the ins and outs of bitcoin wallets etc.) know it's a dead address?
It isn't a dead address at that time. It is just an address that your browser has created, but not yet stored (synced) on the blockchain.info database.
I can't believe $500 can just be lost to the ether like this with nothing to do about it.
People have lost much more. Some of them because they didn't know what they were doing. Others who knew exactly what they were doing, but then made a dumb mistake. With bitcoin you are the only one in control of your money. There is no bank or credit card company to replace your funds for you. You have to take responsibility for your money and make sure you don't do something that you aren't sure about. Making guesses or assumptions when you aren't certain is likely to lead to loss.
How often does this kind of thing happen and why is there no warning or something?
There was a warning. You were told that it was not synced. This kind of thing happens occasionally. More often than I'd like, but not more often than I'd expect.