A forum like this is a good source of general information, not so good a place to get personal advice.
In particular, I am no expert, and I am NOT qualified to give personal advice. And, frankly, I suggest being rather skeptical of anyone who purports to be giving personal advice here.
So I cannot offer any specifics about how things will go for you in particular.
I can offer the following general observations:
1. I read somewhere on the canadavisa forums that I should wait for 730 days (2 years) before I apply for a PR card and not as soon as I arrive, is this true? and if it is, why?
To be eligible for a PR card, a person must be BOTH a PR, and also be in compliance with the PR Residency Obligation. This almost always means that to be eligible for the PR card, a PR who has been in breach of the PR RO should wait, before applying for the PR card, to he or she has been in Canada at least 730 days within the preceding five years, plus a margin actually. Applying before that can trigger a Residency Determination which not only can result in being denied a new PR card, but can result (if the individual is determined to be in breach of the PR RO and not have sufficient H&C reasons to otherwise be allowed to retain status) in the issuance of an enforceable Removal Order, meaning PR status would be lost.
Many PRs abroad who have not complied with the PR RO have, historically, been able to travel to Canada (one way or another) and allowed to enter Canada without being reported for being in breach of the PR RO. Their PR status is good. But they want to avoid doing something which would trigger a residency examination, so they want to avoid applying for a new PR card, applying to sponsor a family member, or leaving and attempting to re-enter Canada, or leaving and applying for a PR TD, for at least two years, until they are in compliance with the PR RO.
You are in a somewhat different situation since your PR status has been adjudicated, and it has been determined you had sufficient H&C grounds to retain your PR status. This decision is, as I understand things, entitled to much weight, almost binding. So you should not be risking losing PR status if you apply for a PR card sooner . . . that is without waiting two years.
But as I tried to explain in my previous post: I am not certain to what extent this will hold true.
Relative to applying for a new PR card, my strong sense is you will be OK . . . but that does not mean Immigration, Refugees, and Citizenship will process your application within the routine timeline. Indeed, I would anticipate some delay.
Best to consult with a lawyer about this, but that could be expensive.
2. Is it impossible for me to leave Canada for a couple of weeks to visit my family and go back to canada without getting into any trouble?
What do you mean by "getting into any trouble?"
If you can travel via the U.S., so that you do not need to make another application for a PR TD in order to return to Canada, and so long as you have established a residence in Canada, and been living in Canada for a significant time, a mere two week absence should not cause officers at the POE to pursue a residency examination, and even if they do, the decision in your PR TD application (the one pursuant to which you now have a PR TD) should be sufficient to avoid being reported. So in that sense, yes, you can leave and return with low risk of being reported, even lower risk of being reported and that resulting in an enforceable Removal Order.
But whether or not you might run into difficulty if you have to apply for a PR TD again, that's another issue and there are risks beyond just the formalities. The formality is that your current PR TD should suffice and there should be no problem getting another (again, if you have a residence in Canada, been living in Canada, and are just making a short trip abroad) . . . but predicting what happens at visa offices abroad is inherently risky.
Better practice: After arriving in Canada, and establishing a residence in Canada, wait a bit then apply for a new PR card, and avoid traveling abroad until you have the new card. It may take a year. Should not be longer than that. If it goes a year, a year you have been living in Canada, you might feel more confident about going abroad and risking having to get another PR TD to return.
Generally, the longer you are settled in Canada, the lower the risks of problems.
3. When applying to university, Am I considered an international student or not? (tuition costs more for international students)
I do not know much about this. My general understanding is that to qualify for resident tuition is that you need to both be actually residing in Canada and have at least Permanent Resident status.
The problem is proving you have PR status without a PR card. Others here may know more about how this goes in practice, what to anticipate, how to approach this.
4. My PRTD expires in 06/06/2016, can I use it to travel to Canada at any day within the 6 months time-frame? (lets say 01/06/2016 for example)
That is indeed my understanding.
Waiting until June next year, however, seems unnecessarily risky. STUFF happens. A few years ago, for example, a volcano in Iceland interfered with trans-Atlantic flights and thousands and thousands of travelers were delayed by weeks, the impact rippling across nearly all trans-oceanic flights to Canada regardless of the route. The more common scenario is a car accident (or other accident, injury while playing a friendly game of football, a bad fall, stuff happens), a sudden illness, the sudden illness of a parent, something which compels the individual to put off travel for days or weeks.