1) Bonjour is pretty easy to tie in with Java apps. If you're particularly masochistic you can write your own Java-based mDNS (Bonjour) responders (I've done it, it's not rocket science), but the quickest way to get going is to use jMDNS in your http server to advertise its existence. I won't copy & paste the code samples but they suffice for most applications.
On the iOS side, NSNetService is your friend. Fundamentally it involves starting a responder in the background to look for services (i.e. your Java app), then calling a delegate when something appears/disappears:
id delegateObject; // Assume this exists.
NSNetServiceBrowser *serviceBrowser;
serviceBrowser = [[NSNetServiceBrowser alloc] init];
[serviceBrowser setDelegate:delegateObject];
[serviceBrowser searchForServicesOfType:@"_http._tcp" inDomain:@""];
There's a guide that explains it all. The protocol hasn't changed for 10+ years and you count on all modern iOS/OS X versions supporting it. The jMDNS library is pretty well battle-tested at this stage, too.
You might consider creating your own service type if you don't want it to be visible to other apps that search for _http._tcp., although this is just a cosmetic thing.
2) The simplest thing that'd work would be HTTP basic auth; you didn't say what kind of authentication your app supports or how you make HTTP requests on the client side, but this is pretty well covered already.
