I am aware of that, as I said before overall erection problem along with lack of morning wood means you
might have erectile dysfunction.
You don't have an overall erection problem. Nope, nada, none existent as of now. But you do have a nonexistent morning erection. But because you don't have a overall erection problem you do not have to worry about the fact you possibly might have erectile dysfunction. Because you don't.
All the erection problems you listed including getting soft after ejaculation is normal and does not pose any problem at all. So there is nothing to worry about there.
If you are really worried you can ask your doctor who will be able to give a 100% correct answer on whether you have or not a erectile dysfunction.
But I am pretty sure. No, I'm definite on the fact that you don't have this disorder.
So relax :]
Cheers,
Peter