Hey there VeF!
Genevieve from Shopify here :)
In terms of apps, MailMunch allows for the addition of custom fields quite easily :) I tested this out and was able to add text fields for 'country' and 'date of birth' to the newsletter signp form, like so: 
You can get that app here: https://apps.shopify.com/mailmunch
I can also confirm that Klaviyo can add the fields you need to the newsletter signup form, with a little bit of custom coding. They have specific guides on how to add these fields:
- Here's their guide on adding custom fields: http://learn.klaviyo.com/14854-Sign-Up-Form-Customization-and-Management/how-to-adding-additional-fields-to-a-simple-sign-up-form
- They even have a specific guide on adding date of birth: http://learn.klaviyo.com/14854-Sign-Up-Form-Customization-and-Management/how-to-adding-a-birthday-field-to-a-form
- You can install the app from here: https://apps.shopify.com/klaviyo-email-marketing
Alternatively, you can customise the Shopify newsletter signup form to collect this information:
https://docs.shopify.com/manual/configuration/store-customization/communicating-with-customers/accounts-and-newsletters/add-signup-form
Hope that helps!
Genevieve S.