Just reading your posts brought back some emotions and I was chapter president twenty years ago! There are a few situations that still sting to this day.
A few thoughts based on my own experiences...
Absolutely have a friend or two outside of the chapter (and preferably away from campus) that will be a safe place to completely dump. You really do need the ability to get it all out with someone safe who will listen and support you.
Do everything by the book. I had to make a couple of very unpopular decisions, one of which cost me dearly. But we did everything by the bylaws and no one could have ever accused me of playing favorites or not doing things correctly. The bylaws, Roberts Rules of Order, etc. are your friend and cover.
I mentioned on another post on GC that being in leadership really does change your sorority experience. Once you take an executive position (especially president) it just isn't the same. It doesn't make it bad, but it definitely makes it different. Only someone who has gone through it can understand. When you are fully aware of all the problems, issues, etc. it is much harder to just enjoy your membership. Being president is a supreme act of service to your sisters. And one that won't be fully appreciated by them or you until much later.
I agree with the advice to try to hang out and do "normal" things with the sisters. It is sometimes hard to fit it in when there are so many other responsibilities taking your time. But making sure everyone knows you are also wanting to be a sister and not just the president is important.
I don't know if you are a person of faith, but I prayed. A lot. And I had a lot of people praying for me in my church and amongst my sisters.
Feel free to come and chat with us here. Even though we aren't there in person, I for one would be glad to be a sounding board on GC.