In all likelihood if you are good at C++, you would be good with C# - 90% of the code you write will be similar and you can look up what the C# equivalent of std::vector is, etc.
Yes. If you've got a good team and a good mentor you'll pickup what they are doing in the first month without too much trouble. But that's not a guarantee.
I could ask you some interview questions about Java that your C++ skills will not help with, so just be honest. I learned on C++, and I though Java was a slow, silly language. But within a few months I grew to love it, and have been using it for a long time.
I will also point out that unless you've been doing correct OO programming with C++, the transition will not be without some trouble. C++ lets you break all kinds of rules: global variables, friend functions, unions, pointer arithmetic, function pointers, casting void* arrays, and all kinds of other things with constructors, destructors, lack of garbage collection, no integrated threading or synchronization library, and a different compile/link/deployment paradigm.