You can use the old Custom CSS/ theme options by exporting and importing through the OptionTree admin screen. That’s the way we do it when we move the content from dev to demo site.
For widgets, you can use the plugin widgets importer and exporter – https://wordpress.org/plugins/widget-importer-exporter/.
I never trusted the DB dump idea with URL replacement and hence always went through the export and import through Tools->Import screen. This works very well if you are dev site is online (not localhost) and the live site is able to import the images directly. Otherwise you will need to spend may be couple of hours of your time setting the featured images after uploading the media files.
The above approach has never failed us although it requires a little bit of work with media files if you are developing locally and trying to move stuff online.
Hope this helps.