1. I want to listen to music on my smart phone.

2. I want to listen to music with smart phone.

3. The baby is playing with a smartphone.

4. The baby is playing on a smartphone.
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Can we use all the expressions?
What is the difference between 'with' and 'on'? Is #3 different from #4 in meaning?

2 is not correct because you need "a" or "the" before smart phone.

Either "on" or "with" is correct in all of the sentences.