Besides the fact that circulating resumes is just about the worst way to find a new gig, I don't understand the mentality that suggests he should give notice before finding a place to land.
Find a new job, then give notice.
I've worked in this field since 1995 and am an employer at a fairly sizable team now and I'll tell you this is pretty close to industry standard. Competent employers do not have an expectation that they're going to get a heads-up before you start interviewing.
Totally tangential to the issue discussed, but years ago I was doing interviews of college kids for dev jobs in a unix env. The recent graduates had had some unix in school, but not much. When asked some questions about it, one candidate let slip that he wanted to see what other people were doing so he started looking in their home dirs.
Was your sister working for you? If so, why? If not, how is this connected?
Also I'm not sure how the existence of a root user plays a part because on the vast majority of unix systems the default home directory permissions are permissive read (this was true in 1987 and is still true now) and if your sister didn't know about root users it seems fairly unlikely that she knew about chmod.
Second this. Nothing more awkward than giving notice and then not finding a job you're excited to move to. Unless your intent is to take a few months off anyway, in which case give a solid last date and make it happen.
It really depends. Yes, if you have a good idea about what you want to do, find a job doing that and give notice.
If you are uncertain, and your current employment situation is feeding that uncertainty, it might be better to get out. I say this as someone who didn't really realize the way I was being effected by my work situation until I heard from a few people who left ahead of me.
0. Get your CV out there
So you can start some leads and if they ask for some weeks notice, you'll have something going (at least some leads) when you're no longer there