The sentences sound 'odd'. I fear, you may grasp the essential meanings and difference between these phrases, but not understand the context in which they are used.
I have no more than 10 dollars
If this is the reply to the question, "How much money have you got on you?"
a native speaker would more likely reply, "About ten dollars, (I think)" or some variation - but far less likely to reply using the phrase 'no more than'.
Girlfriend wants to buy an item at a night market in Thailand, and knows that haggling is part of the shopping experience. She asks her boyfriend how much he thinks she should agree to pay. He replies: "No more than ten dollars." That is, less than ten dollars if she can haggle well, but definitely, not to agree to pay more than ten dollars.
What question did you have in mind, that 'no more than' would be part of the reply?
not more than
With the meaning 'at most':
"We all read about the bomb in the plane that crashed on Lockerbie - you know, some place none of us had ever heard of, the other side of the planet. Then Tom leaves Australia, and is looking for a job in the UK, and ends up living in Scotland not more than 6 kilometers from there. He said, the first few weeks, it felt uncanny."
"The bank says that the time to clear a cheque depends on whether the cheque is from a UK bank or overseas - it can be three days, but definitely not more than 7 working days."
Student or Learner