1
I was hoping you.
I was waiting for you.
Hope means to want something to happen or be true: ‘I hope you are OK.’ ‘I hope the exam is easy.’
Use wait for someone when you stay somewhere until that person arrives: ‘I’m waiting for John. Have you seen him?’
2
I don’t want to fail, but the exam was very difficult, so I hope I will fail.
I don’t want to fail, but the exam was very difficult, so I expect I will fail.
Hope means that you want something to happen.
Expect means that you believe something will probably happen. We can expect something even when we do not want it to happen.
Check our grammar lesson on the difference between wish, hope and expect.