I can see why someone would think there was Terrier, but I'm not so sure about Basenji. (The only way to know for sure is to do a DNA test.) Both of your dogs look very similar. What breed, or mix, is the older one?
We also have a possible Basenji/Terrier (Yorkie) mix. I've had some doubts, but seeing this picture of Rosie, I can't help but see my Rebel. Such a great looking dog, and if she's anything like our girl, you're in for a treat!
Yeah, he loves to chew. Right now it's defluffing tennis balls and cracking them open that entertains him. And chewing on sticks. I do have a kong he loves. High quality treats like pigs ears and such wouldn't do well here as there would be fights over them by all the dogs here, even if I gave each one one, they always want that which another dog has. I do have a few nylabones but he isn't too interested in them at the moment.
Look at the BRAT mixes:
http://basenjirescue.org/DOGS-MIXES/Default.htm
Check out Tia. I think that's what you are looking for. :)
Then look at Tyson and Shiloh. Not the right coloring, but similar build and coat….
