That part I can answer at least. We look, to the best of our ability, because of what a shame it would be if someone, something somewhere, was trying to reach us, and we weren't even trying to listen. If you try and fail at a noble goal, there is some honor and dignity to be had. Nothing but shame if we don't even try. Plus the search for ET has lead to lots of advances in radio telescopes.why
We're looking at earth like planets because the only conditions we know of that support life is this one. Sciencey logic right there. See above. But to go further, the instances that we know that supports life as we know it involve water, adequate heat, a magnetosphere to protect from radiation, stable orbits, stable atmosphere, and probably a bunch of other stuff that someone like Dala or francopoli could pull out of their butts cause this is their area of interest and not mine but I don't have a lot going on this morning and I'm trying to draw a hut (feel like breaking down and just ripping off this guy but I'm actually not a fan of drawing stuff that's already existing) and it's not going well, so here I am, looking for a distraction. SO MANY FUCKING WAYS IT'S MIND BLOWING!!! Off the top of my head, people figure out orbits of planets through the flickering of stars, bending of light, and voodoo science. If a planet is too close to a star, they can probably surmise that solar wind is ripping away the atmosphere and I might be wrong, but I think they can actually take infrared pictures or something to see if it's actually happening. They can also surmise that it might be too hot, too radiated, or in some other way fucked up. As for determining a planet's atmosphere, they have these special spectrometers that look at chemical makeup of shit. I might be wrong, but I think it only works on stars at the moment cause maybe planets are too small or too far or something or maybe we actually do spectrometers on planets, I dunno. That said, if we can see the gas makeup of atmosphere on planets, there might be some tells. For example, the presence of oxygen means it might support life and Dala says that methane is a byproduct of biological chemical reactions so if there's methane there's a chance there's a herd of alien cows farting away to their hearts content. And, as usual, in trying to look something up I find a Wikipedia Article that basically makes an feeble attempt of mine to figure something out, moot.I'm not even sure where, how and why we are looking right now.
Why
How
That's a great point. Of course our "habitable zone" might not be so habitable to another lifeform born of an entirely different environment than Earth's. And think of how weird things might get when you consider regimes far from standard pressure... The recent arsenic-based DNA sham comes to mind (edit: not 'cuz it required non-STP conditions), but hopefully we don't use that to reinforce the notion that our exact organic makeup is the only possibility.
And to expand further, such a quest appeals to our innate humanity. We're naturally inquisitive and to discover other life out there has the potential to answer questions we've had as well as bring about new questions for us to ponder. Despite all of our struggles with each other, we have a natural desire to make connections, to communicate and share our lives with other people. The more life that could be out there for us to discover, the more potential connections we can make. Most importantly though, successful in our endeavors or not, sometimes our attempts to explore outwards allows us to find answers about ourselves inwards.