Is it not supposed to be filled by ntp_adjtime(2). That is what man-page suggested.

After I call auditctl(2) myself, auditing starts in my configured path rather than /var/audit.
But when the audit daemon is stopped and started. Process resumes in /var/audit

Actually:
When the auditd(8) is not already running, everything works fine after running the tests. But on the other side, auditing in /var/audit stops.

So basically, to make everything work normally, we'll have to stop and start auditd8) again. (I verified this behaviour using an independent program).

int size;
if (quotactl("/", Q_GETQUOTASIZE, 0, &size) < 0)
        perror("quotactl");

outputs:
quotactl: Invalid argument

From the man-page, it looks like the error is because the filesystem quota is not already enabled on my system

MAN
The cmd argument or the command type is invalid.  In
Q_GETQUOTASIZE, Q_GETQUOTA, Q_SETQUOTA, and Q_SETUSE,
quotas are not currently enabled for this file system.

No, you're misreading it. That argument is provided from userland to the kernel.

Tough call. Do we skip the test if auditd is already running? Or do we run it anyway, but make sure to restart auditd in the cleanup? I'm leaning toward the latter, even though it will cause a short disruption to the system-wide audit trail. My reasoning is that none of the ATF tests should be run in a production environment, so a brief audit-trail disruption should be ok.

If we're going to temporarily disrupt the audit trail, then we may as well disrupt process accounting, too. You can check whether accounting is enabled with the kern.acct_configured sysctl. Then, during cleanup, either do "service accounting onestop" (if it wasn't enabled) or "service accounting restart" (if it was).

Does that even happen for Q_SYNC?

Are you still working on mounting a filesystem?

I've been trying out numerous variations of commands to see if they execute successfully for mount(2) and nmount(2).

Whenever I get the "type" right, i.e either "nullfs" or "tmpfs", Any other set of command outputs Operation not supported.
For the wrong types, I expectedly get invalid argument