Try clicking on the leftmost button (the one that looks like A/A). This toggles you between WYSIWYG mode and the "plaintext with visible tags" mode.

I have exactly the same problems you describe if I'm in WYSIWYG mode -- no cursor, and new letters appear at the end of text. But in "visible tags" mode, everything is fine. (Unfortunately, you always start in WYSIWYG mode by default, which is rather annoying.)