How to explain to department's president that my time spent as an undergraduate assistant/intern was goalless?
I wonder if anything I say against my supervisor or my experience will worsen my future studies (and relationship) with my professor until I graduate.


It could, and this depends on many factors (including the character of this professor, his relationship with your supervisor, your character and how you explain things etc...), I don't think anyone can predict whether or not it actually will.

I recommend first considering what you hope to achieve in discussing this with the head of the department (aka president/professor). I can imagine a couple of possibilities: 


You feel the need to unload and feel some sympathy.
You care about the system and hope this can be avoided for future students.


If it is mainly the first, I strongly suggest talking to a friend over a beer instead. You'll avoid the risk, and also won't essentially waste your professor's time (which would probably negatively affect his impression of you).

If your motivation is the second, I think this is quite a noble and selfless thing to do, showing high integrity, but it does put yourself at quite a bit of risk with essentially no gain (it helps future students, but if I understand correctly, not you). If this is your goal, I urge you to first consider whether you think this professor would actually care about the advice of an undergrad (I have known professors who would appreciate it, but also some who would simply consider the student to be complaining, in which case relations with that professor would indeed worsen). If you think he will, then I suggest the following:
Before speaking to your professor, make sure you can present the situation clearly, as objectively as possible and concisely (the longer you speak, the more it sounds like a rant and you lose interest - also professors tend to be very busy, and thus have low attention spans for issues that don't seem important). Be very clear straight off the bat that you understand and agree that what has already happened has happened and nothing can/will be done for you, and your intent is solely to raise awareness of the issue so that it can be avoided in the future. Possibly put this intent in writing when contacting the professor for the meeting (again, as short as possible).

In the end, taking action here will involve risk, regardless of your intentions. You will have to weigh how much you care about the issue, and what chances you think you have.