The problem with conjecture about aliens is that, by definition, they're alien, and since we haven't even met one yet (aside from some unsubstantiated claims by some people), we can't even begin to guess at their capabilities, motivations, etc. Remember, we're a primitive race that hasn't even left its own planet, except for a brief excursion to its nearby moon, and some primitive robotic probes to nearby bodies. We really don't know if there's some branch of physics that allows FTL travel, or if it's possible for intelligent beings to exist in multiple or parallel dimensions, etc. Everything we discuss along these lines is nothing more than wild-ass speculation.

One problem I have with your assertion about the ready availability of FTL technology is that I think that assumption relies on the assumption that ETs have similar lifespans as us, which is probably a faulty assumption. A race advanced enough for interstellar travel could very well have totally different biology that doesn't age, or they might have technologically defeated aging, which is something we're already working on ourselves even though we've only sent a handful of people beyond our Van Allen belts. A species that doesn't age, or has lifespans of millennia, might not think it's that big a deal to send a ship to a nearby star system on a journey that'll take a dozen or so years (in ship-time due to relativistic dilation; centuries in planet-time). By the time they get back, their friends might be a bit older, but it'd be like us taking a trip and coming back 5 years later. And don't forget the possibility of "suspended animation". With sufficiently powerful engines able to achieve a sufficiently high fraction of c, a trip of a dozen or so light-years won't take that long in ship-time. It'll even be something we'll want to do with our lifespans.

Discovering our existence shouldn't be that hard. There's hundreds of stars within a few dozen lightyears or so, so an advanced civilization should be able to build a powerful robotic ship to tour them all and gather data. A few millennia or so later, it'll return and they can analyze it, and our existence will be pretty obvious just by scanning the EM range (assuming they came within the last century), or by detecting atmospheric oxygen and photosynthesis. Of course this assumes they're looking for that kind of life, just like we're doing now with our exoplanet searches.

Honestly, it shouldn't be that hard to detect other civilizations from a reasonable distance; we're already detecting various exoplanets, and as I said, we don't even have any serious spaceflight capability; we're doing it all with ground-based and some orbital telescopes. We're having problems seeing planets the size of our own, but better technology should change that eventually. If we had the ability to send a ship to tour the nearby stars and send data back, advanced civilizations should be fairly obvious to a ship inside their system, just by orbiting the likely-looking planets (inside the "habitable zone") and taking pictures, scanning EM frequencies, etc. It would take a while to get data back though since the ship would take decades or centuries to get there.