Staging to live site (Help Needed)

1. There are some Changes in the staging website , I believe changes are mainly theme changes and some new plugin , now the client is asking to make the staging website as live website for that I need to export the whole woocommere products orders and everything into the staging is there any plugin to that ? and it seems for complex

2. If I decide rather than making the staging site live , I can push and theme and plugin changes to live site using staging and wooCommerece stays the same, how Can I achieve that ? Is there any doc or something like that?

I want first to try making changes to local rather than directly to live, if stgaing to local ( Copy of live site ) works then I will push changes to the live site.