The first step for the coughing should be an x-ray. It's the easiest way of seeing directly whether the heart is enlarged, or whether there is a problem with the lungs that could be causing the cough. Yes, I suppose that it's most likely that it's a heart condition, seeing that he's an old dane, but other things should be ruled out.

The thyroid and blood glucose (for diabetes) would be done to look for sources of the seizures, but not the coughing. I'm still trying to think of what blood tests would be done to check the heart - I know one of the labs we work with was offering a new blood test that is supposed to help determine whether there is heart failure, but I don't remember what it actually tested. The heart work-ups we do at our clinic don't involve bloodwork (unless we need baselines for meds) and are always imaging (echo, x-rays if not already done) and EKG.