So I designed a mod on the old site (hoi4modding.com), is it possible to transfer its contents to the Edge so I can keep working on it? and if so how? 

If you export the mod on the old site, you will be able to import the files to their respective tools; you will need to create a new mod here, and a new focus tree/country/etc. for each thing in your mod - but you should be able to import everything from the files.