Hi Small Pink Blob, thanks for your questions:
1) "You've stated that men have to live up to a series of expectations in order to be approved (body language cues, emotional intelligence, positivity, confidence, not being egocentric). In your experience, what are men's requirements for women? What do they expect you to do, say, act like, look like?"
I don't agree (or, if you understood that from my post, then I didn't mean that) that men have to live up to anyone's expectations. My advice before was for men who specifically had problems when they met women because of particular behaviours that are considered strange or "creepy". And then yes, if a behaviour of yours is causing problems in what otherwise is a normal part of life, then I do recommend to modify that particular behaviour. However, for anyone that wants to find a partner, "trying to live up to their expectations on the first date" is going to end up badly, as a partner wants to know the real you. Every woman (and man) will have their own preferences, and it is useless to try to prepare for everyone's preferences. You just have to be lucky and find someone that likes you for who you are. Non-LS people do this by trial and error, and have the advantage that they are born with an innate "confidence" (if you want to call it like this), or lack of extreme anxiety, when they meet someone from the opposite sex. So our reaction to tis is: "well, if he/she likes me, great, if not, I will keep trying".
Answering your question: I honestly never worry about this in advance. The reason is, I don't pretend when I meet a man, I just behave as I am. I wouldn't change my behaviour to adapt to what a man (or anyone else) expects of me. I am lucky in that I have never had serious behavioural problems, and my slight Asperger's traits (the ones I described in a previous post) are almost gone with age. I have no idea what a particular man I am going to meet expects of a woman, but it does not bother me. I am not anyone's expectations, I am myself and I only would want to be with a person who likes me as I am.
2) "About the previous question: Would you say their requirements are too strict or too loose?"
In general (as in particular it can't be analysed), I find most men I meet don't have strict requirements. This may be because I actively avoid men with strict requirements, as they usually are high maintenance, same as women with high requirements, I reckon

. And men and women who have a complicated "list" in their heads about what they expect in a partner usually do not offer the same quality in return, I have found.
3) "If they are too strict: What qualities should women be judged for? What should be the minimum common denominator for women?"
Personal preferences. There are no standard qualities any person "has to be judged for". Some people can't stand people who talk a lot. Others don't like silent people. Others want slim people, others are turned on by fat people. There really are no standards, or if they are, I have as little a clue about them as you.
I believe one big difference between non-LS and LS people (according to what I am reading here) is that LS people have an obsessive worry about these "standards" you talk about. I understand it is difficult not to obsess about the details when something that is so important for you is not working. However, most non-LS people really don't worry about these things that much, or at all. The only women I know that worry constantly about "what the man will like or not" are the ones that have a low self-esteem. I can't speak for men, because I am not one myself.
Have you read the book "The Neverending Story"? At one point, the child-warrior Atreyu has to cross three doors. Each of them involve passing a very difficult test as a person. He gets to the third one, and the test is the following: this door will only open when the person does not want to cross it. He really needs to cross the door to save his World, and he spends hours and hours trying "not to want it to open", and of course, the more he tries, the more impossible it is.
This is the very, very unfair thing I see about people with difficulties to find a partner. other people really don't worry about some things, really don't even think about them at all. They are not interested in pushing that door open, they just go there, and the door opens. I realize how terribly unfair it is. Some of you will have to do like Atreyu, which in the end does cross the door. You have to figure an alternative way to get what for others is easy. But the fact that it is easy for others does not make other people "bastards" and "whores". It makes you unlucky, and it forces you to find alternative ways. The rest of the World does expect a date to be mildly stressing, but not a big deal. They expect having sex to be sometimes a bit of a challenge, but not that hard.
Disclaimer: I am not going to tell you how Atreyu crosses the door, because The Neverending Story is a great book and I wouldn't like to spoil it for anyone whose curiosity has been picked and would like to read it. I will just say it has nothing to do with LS at all, I just used the idea as an analogy.