Hi,
1. It's not data bases but tables. The tables impacted if you only want to migrate the products data are: hikashop_product, hikashop_product_related, hikashop_product_category, hikashop_file, hikashop_variant, hikashop_characteristic and hikashop_price
2. The database is not accessible via FTP. The database is normally accessible via the PHPMyAdmin access provided by your hosting. Usually, it can be accessed through cpanel or a similar hosting management tool.
In PHPMyAdmin, you can export the tables mentioned in point 1 and import the file in the PHPMyAdmin of the other website.
3. FTP won't do for the data. However, if you've also added images or files for these products, these are stored in the media/com_hikashop/upload and images/com_hikashop/upload folders of your website. So you'll want to download/upload them via FTP so that HikaShop can use them with the data pointing to them in the database tables.