Good question. Yes, you are right; it could mean either. 1look at (the dog with one eye). OR 2look at the dog (with one eye). If you want, you can reword it; 2Awith your one eye, look at the dog. OR 1A look at the one-eyed-dog.

I would say that neither of those usages are common English. If the dog has only one eye then you would say: look at the/that one-eyed dog. If you wanted someone to be aware of the dog without giving it all of their attention then you might say: Just keep an eye on the dog (while you are cooking dinner/mowing the lawn/etc.)

It could have either meaning. Only further context would help you. "with one eye" would be physical i.e. covering the other eye. It might be more obvious in speech. It would be more natural to pause after "dog", if you meant use only one eye.

Hello im from egypt and need to practice english whatever you are native or not just i need to practic with person is good at conversations