These are all synonymous so there will be many situations where you can use any of them. Your definitions are pretty accurate, but the actual degree of focus can depend on context. For example, you can "pay full attention" to something, meaning you concentrate on it.
There are differences in idiomatic use. It would be natural to ask someone trusted to pay attention to your child while you are away or distracted for some reason, and you would expect that the person would be completely dedicated to the task. However it would be weirdly excessive to ask them to "focus" or "concentrate" on your child. It would be also strange to ask them to "keep their mind" on the child, as if they were irresponsible and likely to lose focus.
It's obviously impossible to list all the possible ways you would use one or another of these verbs, but here are some examples:
Pay attention to the next part of the video, where you can see the suspect enter the building.
When practicing a piece of music, it is recommended that you concentrate on the most difficult stanzas first, playing them repeatedly until you can get them right. Then the rest of the piece should be easier.
She remained entirely focused on finding her long-lost sister, and every other part of her life suffered as a result.
The teacher warned us to keep our minds on reading our textbooks, but I couldn't help but be distracted by the beautiful weather outside.