This week's book giveaway is in the Other Open Source APIs forum. We're giving away four copies of Storm Applied and have Sean Allen, Peter Pathirana & Matthew Jankowski on-line! See this thread for details.
Java class files have no concept of 32 vs. 64 bit - it makes no difference.
Classes compiled with Java 7 can run on earlier JVM versions provided appropriate -source and -target switches were used, AND the code doesn't use Java 7 features or doesn't use them on earlier JVMs. That's show it has always worked.