As a NES, but not a teacher:
Q1. If the President is giving a speech to the Congress, can we say 'The President is making a report to the Congress'?
A1: Only if he is giving an update on a particular situation (e.g. in his "State of the Nation" speech). If he is just trying to get them to support a particular proposal, then I would not classify that as a report.
Q2. --You'll need to make a report as soon as you arrive.
Does the 'make a report' in this dialogue mean 'to tell someone that you are present and ready for work/duty'?
A2: You would "make a report" to the appropriate person at your destination, giving them an update on a particular situation - See A1, above.
If you "report for duty" then yes, you would be tellng someone that you are present and ready for work/duty.
Q3. The phrase 'make/do a report' in L. G. Alexander's sentence 'I'd like you to check the accounts and make/do a report for me' is translated in Chinese as 'write a report'. Is the translation correct?
A3: Yes. see A1, above.
Hope this helps