When writing a Java program, do I have influence on how the CPU will utilize its cache to store my data? For example, if I have an array that is accessed a lot, does it help
To the best of my knowledge: No. You pretty much have to be writing in machine code to get that level of optimization. With assembly you're a step away because you no longer control where things are stored. With a compiler you're two steps away because you don't even control the details of the generated code. With Java you're three steps away because there's a JVM interpreting your code on the fly.
I don't know of any constructs in Java that let you control things on that level of detail. In theory you could indirectly influence it by how you organize your program and data, but you're so far away that I don't see how you could do it reliably, or even know whether or not it was happening.