Can you be good friends with an ex-lover? Firstly, the word 'lover' has many connotations and the answer may be different for a one-night stand. But what I believe if it's someone who spent a substantial portion of his/her life with, someone who have had a good relationship with, based on shared values, ideas and emotions, a healthy friendship is definitely possible even after they are no longer involved. This is possible because every relationship evolves. If both people concerned have the same level of understanding that they did when they were lovers, it can be used to establish a stable friendship. Of course, if there's any negativity from either side, being friends may not be possible, and that's sad.
When a man and woman relate, there's always a part that is sexual, small though it may be. In most relationships, you tend to suppress the attraction. But when you're friends with an ex, it's much easier to understand and accept this attraction as you've already experienced all there was to experience. In some cases, one person may feel it more than the other, but either way. I think it's much easier to talk such residual attraction through, as you both share a certain level of comfort. Communication is the basis of any relationship.
Even when you and your ex have new love interests in your life, communication is still the key. I believe, for the new relationship to work, you cannot hide your past. The attempt should be not to do things that you need to hide. And you have to resolve the level of importance you want to give your current lover and your ex. Your partner may be insecure, but then we're insecure about so many things in our life. For example, people do compromise their careers for their relationship. So you have to either talk things through with your partner or compromise on your friendship.
As for whether an ex can be a platonic friend who can casually rib you about your present relationship or relate well with your current lover, it's all about the different levels of sensitivity that various people display. The dynamics between your friend, your lover and you will play out according to each person's position in your respective relationships.
I don't think prespectives change depending on your gender. It's about what you believe is right and wrong. If the other person has had a very similar upbringing (although that would be rare), he or she is likely to emote, perceive situations, react and resolve issues just like you would.