Doggengard, I hate to break it to you, but both your dogs really really appear to have been chihuahua mixes. Chihuahuas come in a plethora of colors, not just black and tan or brown or white.
And, chihuahuas are pretty much terriers. So.
Terriers tend to be very strong willed and very active. Be sure you can handle the exercise you will have to give this dog. Both of those breeds need a solid 2 hours a day of exercise and the right motivation.
Basenjis are very quietly, very reserved and very thoughtful. They are pretty much the closest to a cat you can get in a dog.
The bull terrier is very outgoing, they are described as being young at heart and a clown.
Neither of these dogs are 'hypoallergenic'. They just have short hair. You may want to see if you can foster this dog for a while to see how your allergies will do unless you're willing to take shots for them and what not.
For foods, go with something grain free (this helps their skin and coat which will mean less grooming), high protein. If you can get it out of the grocery store, don't feed it.
No, chihuahuas, or at least purebred chihuahuas are from the ancient Mayans in Mexico, and they were not terriers.
Purebred chihuahuas are not terriers. They do not act like terriers.
I should know this, since I have had chihuahuas my entire life so far.
Have you ever owned a chihuahua?
Unfortunately, terriers are now being mixed into the chihuahua bloodline more and more, and I know now how to spot them. If you see a puppy on craigslist or on the Arizona Republic classified ad section and it has the colors of a Jack Russell Terrier-- LOOK OUT! You may not be getting what you think you're getting.
Speaking from experience-- a horrible experience-- if the mixed breed dog has JRT colors it may not end up being the little lap dog you may want it to be. It may end up acting just like a JRT and not a chihuahua.
And yes, they were chihuahua mixes-- chihuahua mixed with JRT and Rat Terrier, and unfortunately, from my point of view, the terrier genes overwhelmed the chihuahua genes, so much that I had to get rid of them.
I was much more careful the next time around and I made sure that the color of the next puppy matched the typical chihuahua breed. And guess what? That's right. I now have a great little lap dog again. A purebred chihuahua this time around.
So, yes, the color does matter. Chihuahuas now come in many different colors, but that's because there has been so much mixing and corrupting of their blood line.