(1) What is a suitable verb for use with 'chart'?
This depends greatly on the context. The one sentence given is not very helpful.
Is that from an email to a friend? Is it part of a business report? A study project?
What was the precise activity? Compiling data? Converting data to graph form? Creating the chart on a computer? All or none of the above?
(2) What is the difference between 'make' and 'do'?
Generally speaking, we use 'make' when we create an object or product, and 'do' when we perform an activity.
In addition, the word 'do' has the general role of a substitute for any verb.
'You need to assemble the data, analyse it and render it in graphical form.'
'OK, I'll do it'.
Later that day: 'Have you done the chart?'