There's a draggable resize handle in the message window, at lower right. And when I enter more text than fits in the window, I get a vertical scrollbar.
What device are you using? Your iPad, perhaps?
Naturally, at this time of the day. I thought the website was now mobile friendly
The other problems with private messages are worse, however. URL's don't automatically become clickable links, for example, and you can't really format anything. You can't attach files or screenshots, either.
When a user wants to start chatting about something in PM's, I usually just give him my email address so we can continue the conversation in a better venue.