Since you bought them from a pet store I would recommend that you take them to the vet to get checked out. Pet stores usually don't know anything about the condition or any underlying issues of their animals. A vet can catch any problems quickly and also assure you that your animals are healthy.
As far as getting them to be comfortable with you, it sounds like you're making great progress. Chinchillas, and probably degus as well, are prey animals and it takes awhile to gain their trust. It will probably take a least a few weeks for them to really trust you. Once you do gain their trust, it is very obvious because they run to great you and instantly want to play. Don't worry about it though, they're just adjusting to new owners and a new home. Make sure you take baby steps and that you don't frighten them and they will start to come around. Also, once they start showing an interest in wanting to come out, make sure that you DON'T let them out until you hold them for a few minutes. They will learn that they must be handled before getting play time and they will hop onto your hand
I'm a chinchilla owner, so all of this information I've gotten from owning them, but I'm sure it all applies to degus as well. I know that chinchillas aren't supposed to eat fresh greens, but I don't know if that is true for degus as well. As for wood, I believe that the rule of thumb is to stay away from citrus trees and trees that have a pitted fruit.
Hope this helps
Oh, one more thing!! Make sure they don't have plastic in their cage because it can be fatal if it blocks their digestive system and make sure that their wheel is a solid surface without any spokes. They can really hurt themselves otherwise.