Can I import certain information from an old site?

You can make your site in a local environment (using something like Local by Flywheel, keep in mind that .htaccess will be needed to be created in a hosting manually: https://wordpress.org/support/article/htaccess/) or like a separate installation at the same hosting with the temporary URL

Running a Development Copy of WordPress

And then use plugin such:
https://wordpress.org/plugins/better-search-replace/
to replace URL everywhere in the database where your site will be moved to the main URL.
You can export from one site and import to another. The first site needs to be available to get images from it. If you have a lot of images, it can take time and didn’t work smoothly from the first attempt, but it should work.

Importing Content

Tools Export Screen

All that you need is somewhere in the documentation.