What to do when theme subscription expires on wordpress? Does it harm?

You can keep using theme without any worries.
Only you will not get more updates on the same.
If you are not worried of new updates then you can keep using.

No, you can uninstall those plugins and search for new and updated plugins as per your requirement. It's also suggested to keep updated yourself about expiries of plugins n updates of various tools which you're using for your blog.