Alors means "in that case," and we often use "then" for that meaning.
"A. She needs food. B. Then I'm going to bring her some."
You can say "well" here, but it changes the meaning slightly. With "then" is means that I will do it because you told me she needs food. With "well" it means that I was going to do it anyway.
Enfin means "at any rate," and that's when we sometimes use "well."
"A. I hope she can eat this. B. Well, I'm going to bring her some."
In the second example, notice that in English you cannot say "then" at all.
¨Lui¨ is used for both him and her when it is used as an indirect object, but in the disjunctive ¨lui¨ means him (e.g. avec lui = with him, but je lui donne qqch = I give him/her smth). In this sentence, the indirect object is ¨lui¨ which receives the object ¨en¨. Here's an article on when to use each pronoun: http://en.wikipedia.org/wiki/French_personal_pronouns