no link mail after PayPal payment

Hey dlikat,
Sorry for the late reply, can I first ask if this is happening to some customers or all customers?
Were you able to test your woocommerce checkout process yourself?
I ask because in my experience of selling downloadable products, some customers do not get the emails because the emails go to their spam folder, or they try to read the emails on their phone.
My next question is when you say:

I do not even have the checkbox to enable automatically sent emails with these links

do you mean that you are relying on PayPal to send the download link? This is not a good choice because the link PayPal sends is very small and is not highlighted, many people do not see this link.
If this is the case then the WordPress email address is not the issue.
If you are having woocommerce send the link then you should ensure that the out going WordPress email address is correct, do you have a log of sent emails? If not then try this plugin to create a log: WP Mail Logging
If you are having woocommerce send your emails, are they sent after the purchase is “compete” which means that PayPal replys back to woocommerce to verify the payment with a IPN. Are you using this setup?

Here is a tutorial on setting up downloadable products with woocommerce, perhaps reviewing it will point out a missed step in your process.

Best regards,
Mike