"This" is analogous to "here", whereas "that" is analogous to "there". If you mentally substitute this/that with "this here" or "that there", one will often seem to be the obvious choice. Another way of thinking about it is if you imagine actually showing the other person the thing you are talking about, would you point to it, or hold it up to show them? If you would point to it, use "that"; if you would hold it up to show them, use "this".
For a concept or idea introduced a few sentences before, I think the key thing is whether it was introduced by you or the person you're talking to. If you introduced it, you're "holding" the idea - use "this". If they introduced it, they're "holding" it - use "that".
As for your last sentence ("Is there a rule describing proper usage of these words in cases like this?") "this" sounds much more natural and correct. I think that's because you are presenting some examples for consideration, so you can imagine that you are holding them in your hand/head and showing them to the target of your question, hence "this".
Interestingly, if I were to then refer to your examples I could use either "this" or "that". Both would sound fine, but have different implications. "This" implies that I have taken your examples/concept/idea into my own headspace to examine and consider close-up, and am still considering them. "That" implies that they are with you, rather than me; either because I'm considering and commenting on them from "over here", as your examples, or possibly that I've brought them into my own headspace, considered them, and have given them back to you prior to commenting on them. Either way, the implication is that they are your examples - I haven't taken on shared custody of them.
Words like egotistic or egotistical ("Believing oneself to be better and more important than others") may apply, as may egocentric ("regarding oneself and one's own opinions or interests as most important or valid") or narcissistic (as used in phrase narcissistic personality disorder). More generally, terms like realistic or unrealistic may apply, depending on whether subject's opinion is correct or mistaken. In some cases, one might call the person a Pollyanna ("person who is persistently cheerful and optimistic, even when given cause not to be so") or Panglossian ("having the view that this is the best of all possible worlds").
Regarding positive or negative connotations of these and other words, among the set of near-synonyms aloof, arrogant, blustery, boastful, bombastic, cocky, conceited, egotistical, flaunting, grandiose, haughty, insolent, narcissistic, ostentatious, pompous, pretentious, self-important, supercilious, uppity, vainglorious, vain, big-headed, high-and-mighty, show-offy, snobbish, snotty, snooty, stuck up, nose in the clouds, holier-than-thou, in my estimation all carry some negative baggage, and those with the least-negative senses include arrogant, egotistical, flaunting, and supercilious; and of those four, only egotistical is adequately close to the meaning requested in question. Note that self-righteous is a rather more negative label than egotistical. Realistic, if you can apply that label, is positive or neutral, and unrealistic is negative or neutral.
I have said terms arrogant, egotistical, flaunting, and supercilious are less negative than others, partly as a consequence of how similar terms are used in Aristotle's Nicomachean Ethics, as for example the lengthy discussion of pride in Book IV part 3. However, the slightly-technical usage there is uncommon, so only a weak basis for comparison.
Best Answer
In a criminal trial in England and in many other English-speaking countries which have a legal system based on what is called the Common Law, there is a single judge and a jury of (often) 12 people. The judge is legally qualified and controls proceedings and makes decisions on what the law is and give directions to the jury. The jury consist of ordinary people selected at random and the jury decide which witnesses they believe and, ultimately, whether the accused is guilty or not guilty. Some civil proceedings also use judge and jury trials.
In the context of a company internal contest it would be fine to use either "judge" or "jury" but "judge" is slightly more common if there are a limited number of people (e.g. up to 3 or 4) and jury would be slightly more usual if there are, say, more than 6.
Also you might be more inclined to use "judges" if the contest involves the judgment of technical skill and slightly more likely to use "jury" if it is more a matter of opinion - e.g. the best song.
But basically either "jury" or "judges" or "panel of judges" is fine.