Are you trying to write in the right place?
I must admit it's not an easy message screen. Where it says send message click on that first it opens up the place to write your message. Write your message then the blue arrow on the right.
The above is when you use a laptop /PC sorry I don't use the app, it may well be different or causing issues there.
Try Chrome as a browser too, it seems to work well with eBay.
@siennastar-123