已通过 is not right here since we're showing this message telling the user that Brackets will provide live preview in the browser.
修改预览也将修改你的代码 has the meaning flipped. We want to tell the user that your changes in Brackets will also show up in the preview in the browser.
之前的版本 {APP_NAME} is totally misleading. It's not _previous_ version that we're referring to. We're trying to say that current version is an _early_ version (and not a full-fledged version).
和 in 实时预览只能运行于 <strong>Google Chrome</strong>浏览器和更新实时编辑时的 <strong>CSS 文件 may not be correct. I know English version uses "and" and its meaning is 和, but here we're telling users that live preview is only limited to Chrome browser and is only capable of showing live updates in CSS files (not other types of files).