Not easy questions. Philosophical accounts of happiness have tended either to stress happiness as a subjective matter involving (for example) the satisfaction of preferences and desires or in a more objective or less subjective matters, for example, a person is happy if she is flourishing. Subjective accounts tend to give more authority to the person's own self-evaluation, e.g. you seem to be the best authority when it comes to identifying what you desire or prefer. But subjective accounts may still distinguish between what you actually desire or prefer and what you should desire or prefer if (for example) you knew more of the relevant facts. Thus, you might desire to marry Fred but (unknown to you) Fred is a terrorist and you most emphatically do not wish to marry a terrorist. A subjectivist might also allow for self-deception. In such a case, a person may think they are happy because she believes her main desires in life are fulfilled and yet those desires are the result of some self-created impairment (you believe you want to marry Fred but this 'want' is based on a dreadful fantasy that you have invented).
I am inclined to a somewhat less subjective account. So, the subjectivist may be right that happiness involves our preferences and desires, but the kinds of preferences and desires that are truly conducive (or partly constitute) happiness are those that contribute to a person's flourishing. What is flourishing? Not easy to spell out, but I believe that Aristotle gets us off to a good start in his Ethics in his treatment of the actualization of your powers (of reasoning, thinking, perceiving, acting with prudence, temperance, justice, courage). From an Aristotelian point of view, you may grow in happiness insofar as you flourish, realizing the great practical and intellectual virtues. Knowing whether you are flourishing may require a mix of self-awareness as well as living in a community in which persons care about and reflect on the happiness or wellbeing of its members.
I am not quite sure what you are looking for in terms of limits. Maybe it is useful to distinguish happiness and being healthy. I believe we have good reason to think that sometimes unhappiness is healthy and good, as when we mourn or grieve the loss of someone or thing we love. In light of that, maybe we should think that the limits of our happiness should (in some sense) be determined by our own and others' health or overall wellbeing. It would not be good (it would, in your terms, surpass the limits of healthy happiness) to be happy in the face of profound tragedy. Ending on a lighter note, it also may in some sense be a duty to try to be happy (or to try to try to be happy) in the presence of great goods such as young, healthy children, romantic love, courageous compassion, and an illuminating philosophical dialogue.