K.K.
It will be awhile before the animosity your step daughter feels towards your son lessens (and maybe goes away).
It is a natural feeling and it does not only apply to step children. My oldest child is 7 years older than her twin siblings. She was effectively an only child before they came along and it affects how they interrelate.
4 years later it has decreased significantly, but there are still issues. My oldest has many chores while the 4 year olds are just starting to help out with them and have 1 or 2 of their own.
Regarding "fairness" of chores situation. Have a family meeting to discuss who does what chores. Let the kids pick (to a degree) which chores they want. Make a list of what chores you expect them to do and see how they split them up. Make a visual aid for them that shows who does which chores on which days with a place to mark if it has been done. Offer a reward (computer/video game time, allowance, special tv program time, movie, etc) for the comlpletion of their chores at the end of each week. Or a token system allows for them to earn a token for each chore completed and they can turn in tokens for rewards (allowance, movie, computer/video game time, etc). This should encourage your step daughter to participate and to feel things are being looked at a bit more fairly. Perhaps you can offer a equaling of things to help out. She earns two tokens per chore because she is older, or because she does more chores.
Sharing. Have a discussion with her one-on-one to determine what 5 or 10 items are most precious to her that she feels she absolutely should not have to share with your son (make sure you give your son this same option as well). Then explain that because you are all a family now, many things need to be shared, but that the 5 or 10 things you discussed will be hers alone to keep to herself. This gives her a sense of control over her things while encouraging her to share the majority of things in the family.
For the fact that your son idolizes and wants to spend time with her, while she shuns this...You can talk with both of them together and explain to her that you understand she did not have a brother before now that wanted her time and attention, but that your son sees her as this wonderful person to play with and learn from. Then explain to both of them that there is part of each day that is "me" time. This means that he cannot bother her no matter what, and vice versa so that they can do things on there own, but that for a half hour or an hour each day you would like them to do something together (a project, playing a game, playing outside, anything that promotes getting a long and being together). It will have to be forced and enforced at first, but once they start doing things and she sees that she gets time that doesn't include a "tag-a-long" you will see that it happens more and more naturally.
Including them in these discussions allows them to feel that their opinions and ideas matter to you (we see it when you write to us, but sometimes our families don't see it) and may help her to become more family oriented..
Good luck... ;-)