Refactor options page to use Typescript

Also, I've added and ran eslint, and fixed several minor issues accross
the Typescript codebase.

Bug: translateselectedtext:15
Change-Id: I8cfd67697f9bfb22f6de93b64fd750de66bab863
diff --git a/webpack.config.js b/webpack.config.js
index 239fc73..f5d0010 100644
--- a/webpack.config.js
+++ b/webpack.config.js
@@ -9,7 +9,7 @@
   // web_accessible_resources in //templates/manifest.gjson.
   let entry = {
     background: './src/background.ts',
-    options: './src/options/options.js',
+    options: './src/options/options.ts',
   };
 
   let outputPath = path.join(__dirname, 'dist', env.browser_target);