How to allow customers to register without providing phone numbers and an address in PrestaShop
PrestaShop 1.5 introduced some new settings in the admin panel. Some of these settings allow you to easily include or exclude the address form on the registration page and to make the phone fields required or optional. To access and modify these settings, log in to the backend of your PrestaShop and go to Preferences menu>Customers. There you'll see the options Registration process type and Phone number. To exclude the address form from the registration page set the option Registration process type to Only account creation. Customers then will have to provide an address while checking out for the first time.
If you want customers to be required to provide an address while registering set the Registration process type option to Standard. The phone number fields are part of the address form, so if the customer has to provide an address, you can use the Phone number option to specify whether the customer is required or not to provide a phone number.
The Phone number option also affects the address form in the customer account settings of registered customers. So, for example, if you set it to No, registered customers will not be required to provide a phone number when they add or edit an address from their account settings.
Older versions of PrestaShop don't have these backend options. By default, if you use a version older than PrestaShop 1.5, an address form is included on the registration page. For information on how to remove or make optional the phone fields on the registration form in these older versions (e.g. PrestaShop 1.4), check out the article on removing the phone fields or making them optional on the registration form in PrestaShop. In case you use a newer version (e.g. PrestaShop 1.5), you've included the address form on the registration page by setting the Registration process type option to Standard, but you want to completely remove the phone fields and not just make them optional, you'll also find that information in the above mentioned article.
For similar information but concerning the customer account settings check out the article on removing or making optional the phone fields in the customer account settings in PrestaShop.