Hi there,

#1. Please go to Apprance -> Customize -> Woocommerce -> Catalog -> Select show category in shop page: https://prnt.sc/vl6hf1

#2. Please go to edit header page http://bikehouse.pt/wp-admin/post.php?post=1407&action=elementor#
Edit Logo and change your size logo: https://prnt.sc/vl6n2z

#3. Yes, go to edit header page, add social icon for top header bar: https://prnt.sc/vl6o9z

#4. I don’t understand your question.
Do you want to import data product from your site into this site?
Use plugin WooCommerce – Product Importer

#5. Please view guide at https://docs.woocommerce.com/document/variable-product/