Did tom mix have a dog?

If by "bird dog" you are referring to a dog (like a Brittany spaniel) who works with a hunter to flush out and catch birds, or a pointer who finds birds... and if by "weenie" you mean dachshund, then...

Yes but there might be difficulties. The female dog has to be the medium sized dog because if the male is quite a good size bigger than the female then the female's puppies would be too big for her...

I can definitely see some Beagle in both of them - they have the classic ''Hound'' colouration and they look like they may be Beagle sized. However, the long fur on the tail and ruff suggests a breed...

Practically all mixed dogs have a mark on their tounge. It is not pure pink. This is a way you can tell pure bread from mix.

Many dog breeds can mix. For example, the dachshund and the pit bull are mixed breeds of dogs, but there are many more.