We can't assist with Profile Pro. CB is no longer responsible for the profile rendition when such extension is in use and thus we can not help you. If issue is present without the usage of Profile Pro we'd be glad to help. Please contact the developers of your extension for support.
For example a member has the option to give a mobile number in the registration process. Now if the person doesn't submit a mobile number the field title "mobile number" will still show up on the profile page. I want to have a field title, but it should only show up if it includes information and is not just empty. How can I do this?
For CB (not Profile Pro) this is configured within CB Configuration on the User Profile tab to not display empty fields.
The other thing I would like to know is how I can allow new members to upload pdf files to their profiles. These will include their product prices etc.. Is there a plugin for this? I searched the forums and couldn't find anything regarding this.
For CB (not Profile Pro) this can be done using documentation subscribe CB ProfileGallery in file mode or documentation subscriber File Fieldtype plugin which allows adding File fields similar to that of Image field usage, but for files.