What’s written on the tag? Is the scarf it really 100% cotton and dies it feel like real cotton?

Can’t see a tag on the scarfs. It could well be Very thin cotton. Can’t say for sure.

Does this shrink upon washing?

On a gentle cold wash or hand wash NO it does not shrink! I put all of mine in a mesh wash bag and line dry. Hope this was helpful

where is this scarf made and shipped from?

The scarf does not have any tags on it to say where it was made. I bought it way back in 2019 for my husband who went through radiation a chem for laryngeal, (throat cancer) I wanted something so he could cover his throat and protects it from the sun. The doctors said he had to do this for at least a year. I also don’t know where it was shipped from. The material is pretty thin but it is wide so it can be folded over and it is pretty long so it will wrap around. Sorry it took so long to answer. I’ve been a little busy and my husband had put it away and he had to find it.

Why is this a square? It's advertised as a rectangle.

This is the typical long scarf you were around your neck, like a winter scarf, except it is in a very lightweight fabric. It's an accessory worn for style, not for warmth. It is not a square or rectangle, like a pocket square or handkerchief.