Go to ReSharper | Options. Change the following options:
On the page Environment | Editor: turn off options that starts from "Auto-format" or "Auto-insert". This won't disable ReSharper formatting features completely, but at least they won't be invoked automatically when typing.
On the page Intellisense | General: change to "Visual Studio". Or, if you only dislike code completion in JavaScript, change to "Limited ReSharper Intellisense" and turn off JavaScript.
P.S. Could you please describe with examples, what do you type when ReSharper is "stealing braces". Thanks!