Basically your product predates theirs and you have a case. Also let the lawyers handle any communication as you may be stepping out of bounds. (let them handle it)
And be happy that someone is copying you, It's a sign of flattery. Plus they have made their Android users as a few marketers for you for free. Every time an Android users comes in contact with a iphone user who appreciates that app they will look for it in the iphone app store.
good luck.
If they wrote an app that looks like yours, most likely they've done nothing wrong. Many apps have only one look. Calculators for example. They all have similar or the exact same buttons, layouts, colors, etc.
You can take it as a badge of honor that someone liked your idea enough to copy you. I've had one of my iphone apps copied, not quite as thoroughly as you say, but enough to know that I inspired them. I say, have at it - if they're making the same kind of money I am from it, it definitely cost them more to make than it's worth. ;-)
Again, not a lawyer, I could have said something completely wrong, but as far as I know what I said above correct.
What I would do in your shoes - obfuscate the code if possible, iterate rapidly (nobody can execute like you), and move a lot of logic to the backend where nobody can steal your code.