Can I restore apps from my SD card? I was a bit quick to switch phones, is it possible to restore the applications with their settings from the SD card (When they were installed on the card, ("regular" and Link2SD).

(I can of course get the apps from Google Play, but I would like the "old" settings to come back)
As you no longer have the original device, you've lost one option: Backing up those apps using Titanium Backup ★ root, sending those backups to the new device, and restoring them with the very same Titanium Backup.

If you didn't back up your apps before turning the device in, it's like asking: "I just burned those papers. Can I still get a copy of them?" At least the "regular" ones are gone that way, as apps2sd only moves a part of the app to your card. An essential part (including the app's data) is left in internal memory.

Still having your card, it might look a little different for the Link2SD part: Here you can at least pick the .apk files from your card, as they are still there. Unfortunately, the same cannot be said for their data: Link2SD does not move application's private data files; it moves apk, dex (dalvik-cache) and lib files. (from the Link2SD app description on Google Play).

If you additionally used Root # All Data2SD card., it's again a completely different thing. In this case you should be able to re-install the app from the .apk, Link2SD it again, Data2SD it, shutdown the device, put the SDCard to your computer via a card reader, replace the data directories from the copy you've made of the old SDCard, unmount safely, put the card back to your Android device, and start it up.