I'll stick with my comment that, as a starting point for discussion, an issue is, in one definition, either a vital matter or an unsettled matter. (See here, at 6b for example.)
Also consider that people are naturally prone (in my U.S. English experience, anyway) to use exaggeration for effect, either to sound humorous, to be emphatic about a point, to communicate in a thought provoking way, or to provide metaphoric imagery.
That being said, I would say that your example "I will have issues with the clock" veers in the direction of exaggeration, stating that something of vital importance (as in urgent, pressing, compelling) is associated with the clock - there is a meeting scheduled. This fits perfectly within the inclination to use a figure of speech for any of the purposes I mentioned above.
When Suzannah has issues with self-confidence, she has an unsettled or unresolved matter concerning her self-confidence. There is a problem, question, or dispute about the state of her self-confidence.
If you say you have an issue with another driver, then someone would infer that there is an unsettled matter (a problem, question, or dispute) between you and that driver.
An issue with one's heart is a vital matter in the most literal sense, but to say there is an issue with one's heart is also to say there is an unsettled matter with the heart, just as above.
None of these examples are even a far stretch from the cited definition of the word issue. As to how far you can go, the limit is determined by the point where you cease to be understood. English users love to engage in figures of speech and will even invent their own at times (and there's no reason not to, aside from reaching the point of being incomprehensible).