If you find difficulty in updating using toolkit method then you can do the following –
You can’t remove an active theme, so first activate the default WordPress theme (Twenty Fourteen) to be able to delete a theme required. Click the deactivated theme to see it’s details and click Delete button in the right bottom corner of it. Use the same procedure as when you installed the theme for the first time.
Everything you did on your Dashboard won’t get overwritten, the files you’ve modified, however, will be replaced with the new files.
I recommend that you save them in separate folders so you’ll have them at hand to reapply the changes. If you made any changes to the source files (instead of child theme), you will need to redo them of course no matter what method you use for updating.
Regarding custom CSS backup – Just copy the custom CSS in a txt file and save .