Typing in Web Browser (Firefox and Chrome) Text Boxes and Text Areas on Android is Awkward
You don't need to drag the placeholder, in a text area whose content is larger than the editing area, you can scroll the text by dragging on the editing area itself. This works in both Firefox and Chrome for Android.

Regarding to text area resizing, yes, this is possible. Resizable text area works in both Firefox and Chrome for Android (demo), but they must be enabled by the website with a CSS3 code.

If the website you frequents doesn't enable text area resizing, in Firefox Mobile you can use the Stylish Add-on to force all text area to be resizable with a userstyle CSS like the following:

textarea { resize: both; }


Stylish add-on is fully supported in Firefox Mobile.

AFAICT, Chrome Mobile does not support Chrome extensions.