Any ideas what the ghost of her twin sister does?

The only effect I noticed so far what that when I move right next to it, I die :(.

She's a helpful ally - she can fight enemies for you. You cam read more on here [url=[url=http://dont-starve-game.wikia.com/wiki/Abigail)here[/url]http://dont-starve-game.wikia.com/wiki/Abigail)here[/url[/url]].
From the fact that your Wendy is killed by her, I suspect you don't have the latest update ("Strange new powers"), which GOG doesn't provide yet. You can get it using the updater provided with the game and inserting the code you got with Don't Starve.

On the one hand you should be glad you died quickly at the hands of Abigail prior to the latest version. She was so damn irritating it drove me insane (and I don't mean in the game!). Apparently she's a lot less annoying now, plus she won't harm you or your allies.

Thanks for the replies.

I reverted back to playing with the original character for a challenge (and because I wanted to see what shaving the beard does), though I must admit I was fond of the strong man for his ability to beat up critters in the early game.

I played him a lot actually prior to the latest update. I found the beard to be extremely useful in winter, as it provides more insulation than a winter hat (but not as much as a beefalohat or a puffy vest). So even without a heat stone or any other insulating clothing you can wander around a little bit before freezing in winter - and if you have a beefalohat and a heat stone, you don't need a vest of any kind to wander around for ages, so you can use a backpack for a long-ish winter journey.