'Irrealistic' or 'unrealistic'?

Solution 1:

The word realistic is negated with the prefix un-, which is not the same as in-/im-/ir-, and is not subject to the rule regarding in-/im-/ir-. The rule that you cited is correct, but only for words that take the negative prefix in-/im-/ir- (e.g. intractable, impossible, irresponsible). Words that are negated with un- always use un- (e.g. untreatable, unbearable, unready), and never vary the second letter of the prefix.

There is no general rule that will allow you to know which words take the negative prefix un- and which take the negative prefix in-.

The forms that you find on the net with the word irrealistic are either mistakes by non-native speakers, people being clever with word-play, or possibly people creating derivations off of the specialized linguistic term irrealis.

Solution 2:

Yes.

Never heard of such a rule. Or I may have forgotten about it. Never been a fan of rules about language anyway: you learn the rule and the myriad of exceptions (depending on rule and language in question)- Why not just learn the words, and be done with it?