Upon searching for a fast primr algorithm, I stumbled upon this:

public static boolean isP(long n) { 
    if (n==2 || n==3) return true; 
    if ((n&0x1)==0 || n%3==0 || n<2) return false; 
    long root=(long)Math.sqrt(n)+1L;
    // we check just numbers of the form 6*k+1 and 6*k-1 
    for (long k=6;k<=root;k+=6) { 
        if (n%(k-1)==0) return false; 
        if (n%(k+1)==0) return false; 
    } 
    return true; 
}

My questions are:

1. Why is long being used everywhere instead of int? Because with a long type the argument could be much larger than Integer.MAX thus making the method more flexible?
2. In the second 'if', is n&0x1 the same as n%2? If so why didn't the author just use n%2? To me it's more readable.
3. The line that sets the 'root' variable, why add the 1L?
4. What is the run-time complexity? Is it O(sqrt(n/6)) or O(sqrt(n)/6)? Or would we just say O(n)?