Due to a lack of agreement on the 'killing or not' part, I'll go with two things:
Looking out the window
Trying to find out weaknesses.
Letting your shapeshifting trials stop for a moment, you try to concentrate on the important parts: What kills you? Well, you don't know yet, you've never been killed. However, you can try to make one or two guesses.
You can change your skin itself to be more resilient to weapons, at the cost of appearing like scales or plates. However, you're not sure if it's actually necessary to do so - your body itself is homogeneous, without blood or any major organs - unlike mortal bodies. You just know you heal fast - or actually, they heal slow - so with a bit of rest you should be up again after half a day or so. And, if the book is to be believed, you can't be killed permanently without some ritual to be performed, but return after a century or so. You really, really do not want to test that.
Still thinking about those facts, you step to the window, to look outside. It's late in the morning, on a nice spring's day. You now find your assumption confirmed: You really are on an island. The ruined fortress your tower is in is on a land tongue, extending far to the south east, and forming a big, sheltered bay, in which a small village lies, about ten kilometres from you. You can clearly see two big ships, probably traders, in port there, and a couple of smaller anchorages, probably for fisher boats. You even see the trader's crew, seemingly fixing minor damages, probably from a longer tour. Some fields are near the village, and a mountain range crosses the island and seems to divide it in two. The island is forested, and especially the land tongue the ruin stands on, with just a small path leading through it.