Do these have a cotton liner?

They do have a small cotton lining in the crotch...for all the good it does. It covers a pretty small area, and in my experience, doesn't go up far enough in the front.

Size chart for these panties?

The size was the same as others I have purchased, but it didn’t say that they were low rise. They also ride up in the back. Nice, light fabric, but they scrimped on the elastic and trim on waist and legs.

Can anyone tell me the sizes, how they run for medium and large. I’m not seeing a size chart.

They do NOT run true to size. Maybe if you are very tiny they might but if you are a size Large or 7 panty they do NOT fit right. THEY can be stretched to fit anyone yes, but they are so thin material they are almost like wearing nothing and see through. I have other panties made from the same materials that are much thicker and fit right for my size. But these were very disappointing to me. I'm returning mine. I am older and do NOT want see through undies. I have to stretch these so much to fit me because they are so tiny that they end up NOT being a brief by the time I have them on. They look like very high cut panties and very small and sheer. Not covering very much really. A big disappointment to me. I only bought these after carefully studying the materials and other things to be sure they'd be exactly like what I have now or very close. BUT they are not even close to what I have and what I like. The percentage of the materials that are listed here are incorrect. They are different percentages but even with that they should have still been okay but they are NOT worth the money. If you like sheer undies that do NOT cover you like a brief should. I would at least suggest you buy a size or even 2 sizes up if you are a size Large like me. (or a 7 panties) I hope this helps someone.