Can anybody help me with a solution to remove the shipping price in the checkout process, and also in the order email. Right now it is set to 0,00 but I want to remove the price, so only the delivery text is displayed.
On the orderemail go and make a new email template. configuration --- > email.
There you can import magentos template and modify like you want. Just remember to go under sales-emails and choose your new template.
for the frontend, i would display:none, its the easiest!
You can easily hide it using CSS because you want to keep the shipping method text.