Genetically, they should all be able to interbreed, also with wolves and coyotes.

However, there are quite a few breeds that are known to have breeding and birthing problems. Some unable to properly mount each other and breed. Others with hips too small to properly birth and need close to 100% C-section delivery. I can imagine these problems could be exacerbated by attempts to breed with other larger breeds.

Not at all. Domestic dogs, coyotes and wolves can all breed together.

Nice! Thanks!

Yes. The pairing would probably be a male from a bigger breed and a bulldog bitch as the latter often can’t give birth without a C section. So, sans technology, I can imagine there are at least a few pairs where offspring wouldn’t happen.

I don't know if this counts, but a lot of bulldog-like dogs can't give live birth because they're so deformed and unnatural. They can only give birth by C-section.