Is this a sticker label?

Yes, our Standard White Matte (WX) is considered a sticker label with a permanent adhesive. If you'd like to try samples of this product, please feel free to visit the link below to request a few sheets at no cost. https://www.onlinelabels.com/samples

How would this label do when applied to muslin/fabric? would it adhere well?

While we haven't tested our OL3187BK labels for this type of application, the Brown Kraft labels feature a permanent adhesive that will work on a variety of surfaces. If you would like to test these labels with your application, you're welcome to utilize our sample request form. https://www.onlinelabels.com/samples

I use the weatherproof polyester label sheets for my lotions, lip balms, etc. How would this material stand up to being smudged from oils in my products?

The Weatherproof Polyester Laser (LP) is very durable and the material itself will not break down when exposed to oil. Although it is possible that the toner from your laser printer may react to the oil and cause discoloration, so samples would be recommended. You are welcome to request free samples for testing with your printer by visiting the link below. https://www.onlinelabels.com/samples