I read about the naming of Java variables. It says that Java variables cannot start with any numbers and special characters except for $ and _.
Some valid examples:
int count;
int _count;
int $count;
And some invalid examples:
int %count;
int 4count;
int #count;
Do the same rules apply to method names?
Yes, method names and variable names are what's called "identifiers". Identifiers all share the same rules regarding accepted characters. Take a look at §3.8 from the Java Language Specification to find out exactly what an identifier may contain, and §6.2 for an explanation about how identifiers are used.