When you increase the number of frames, using $FIFO$ can sometimes result in increased page fault due to Belady's anomaly .
This does not occur always. Hence, $S1$ is false .
Loader is responsible for loading a process which is supposed to execute on $CPU$ from the main memory. So, it is necessary for Loader to be in main memory. That makes $S2$ also wrong.
$S1$ is also wrong because the number of page faults depends on the reference policy we use. But here, they mentioned it as irrespective of reference policy.