a) Do you think it is possible to search for extraterrestrial life with our current methods? I know that SETI aims to track alien life by scanning the cosmos for any stray radio signals that might be a sign of intelligent life.
Of course it's possible. We've been doing it for more than 50 years. Whether or not we will find anything if it's out there to be found depends on several factors, but the primary ones are, how far away is the nearest extraterrestrial civilization, and is it using a technology that we could detect with the instruments that we are using?
b) Would we even know what extraterrestrial life would look like even if we came in contact with it?
Poorly worded question; it really conflates two ideas.
Q1: Would we know what to expect before we came in contact with it?
A1: Not necessarily, unless it's carbon-and-water based and lives on a planet broadly similar to Earth.
Q2: Would we recognize it as life once we saw it up close?
A2: I find it difficult to imagine that we would not. Perhaps not instantly, if it operates on a time scale vastly slower than our own, but eventually we'd figured it out.
Would we even be able to communicate with such a sentient alien life form?
If it's sentient enough to form a civilization, we will at least be able to exchange algebraic proofs with it, even if we have nothing else in common to talk about.
c) And as a random throwaway question, if said extraterrestrial life were sentient, do you think it would be acceptable to form sexual relations with them?
I think the main moral objection to sex-outside-your-own-species on Earth revolves around the idea that humans are the only sentient species on the planet (that we know of), and therefore the only ones capable of clearly and unequivocally consenting to sexual relations. I would assume that similar arguments will be made for extraterrestrial species. If it consents, I don't see how having sexual relations with it poses a moral problem. Plumbing is another matter.
d) What do you think of the current 'evidence' offered by those who believe that aliens have been in contact with humanity (e.g. Roswell, ancient aliens, UFO sightings, abductions, etc)? Personally, I think they're unsubstantiated for the most part, but they are interesting to think about.
No reliable, tangible evidence has been offered, which is remarkably hard to explain if we have in fact been visited and probed as much as some UFOlogists claim.
e) Here's a scenario: if an alien spacecraft landed on planet Earth, what do you think our first cause of action should be? And on a personal level, would you go batshit crazy and panic, locking your doors and stocking up on ammunition and rations?
Assuming that they not not land outside of London and immediately march on it with tripods wielding death-rays, I think our first action should be to attempt communications. My personal reaction would depend on an assessment of the risk that they pose to life on Earth, and my own hide in particular. I would definitely not assume that they are hostile without some overt sign that this is the case.
Last night I was going to make a thread about question (a), but I decided against it. I was thinking about how in parts of sub-Saharan Africa they used drums to communicate quickly over vast distances, but to non-Africans, they couldn't work out what the messages were saying and for quite a while didn't even know the drumming had any purpose. So, that line of thinking brought me to a criticism of SETI I've had since I was about twelve years old. They're spending all this money on searching for alien civilisations, but they've assumed that aliens would have naturally developed the usage of radio signals to transmit messages. They have just assumed that other species develop concordantly with us. It seems like a massive waste of money to me.
Any alien civilizations will have to make use of the same physics that we do. They will necessarily have to go through a phase of using radio technology (nothing else is this obvious, this useful, and this easy to do), although they (and we) will probably move on to other things eventually. Tight-beam laser communications come to mind. But radio communications are too cheap, easy and effective to ever give up entirely, although they may be relegated to low-powered systems for communications over a span of meters rather than continents, and thus impossible to detect over interstellar distances.