Normally with these sort of things, I like to hit a lot of different dictionaries. Here though, the definitions you give tell it all:
very confident and direct about saying what you think, in a way that is not socially suitable
(of a person) bold or overfamiliar in manner: I am not usually a forward sort of person
(Emphases mine)
In the definitions you give, the fact that forward contains an excess that makes it unwelcome is given clearly of the definition. It's also implied in the example, as it wants to deny the quality - which we would of a negative excess, but not of being honest and direct.
The classic example of a straightforward person, is the sort of characters James Stewart used to play; politically open rather than manipulative, not given to intrigue, and likely to say "well, 'cos I think you're a fine looking woman so I'd be mighty pleased if you'd accompany me" rather than subtly seductive.
That last bit is the closest those characters to being forward, but they'd be horrified and apologetic if it was suggested that they were. A forward person shares the bluntness of the straightforward person, but will continue with advances to a degree that seems creepy, or where the a straightforward person would be honest about personal matters, the forward person would be honest about personal matters that have no bearing on the conversation and at a time when it is not appropriate to bring them up.
So while the forward person is indeed honest and direct, this unpleasant excess is a core part of the definition. Since honesty and directness are generally considered positive qualities, it's not reasonable to consider it a valid Jeopardy answer for that definition.
I would have also picked everywhere and nowhere if forced to choose between those options. But I wouldn't have been happy about it.
Without actually looking at a thesaurus, when I hear the word irrelevant I think to myself immaterial, unrelated, not useful, beside the point, off topic, and has no bearing. Only one of those is what Wiktionary lists. Further, I would never associate irrelevant with impertient—so I find that synonym strange. (But that's just based on my personal associations.)
By the process of elimination, I immediately ruled out the first four possible answers. (Unlike the Italian student, I would never associate irrelevant with inappropriate. That word has a negative connotation to it that I don't get from irrelevant.)
That left me only with everywhere and nowhere.
When I hear everywhere and nowhere, I think to myself unhelpful and meaningless. Those are at least close to irrelevant—and certainly closer, in my mind, than any of the other options.
But, as I say, it's more a process of elimination for me than an affirmative statement. (A kind of two-step equivalence.) Everywhere and nowhere is certainly not something that would leap into my mind as meaning irrelevant.
Having now composed my answer (not having wanted to have research affect my subjective response), I see that Merriam-Webster shows the following in its thesaurus for irrelevant:
Phrases Synonymous with IRRELEVANT
beside the point, neither here nor there
I note that neither here nor there has almost the same meaning (or non-meaning) as everywhere and nowhere.
Best Answer
The Oxford Learners Dictionaries defines worse as, among other things, less good. So I suppose if OLD can use less good, so can we. Still, when comparing two good things I would say:
My admittedly foreign ears don't like the sound of less good than. Google search concurs: not as good as beats less good than 6,000 to 1. This English Grammar advises against less good than on the grounds that "[w]hen making negative comparisons less tends to be used only with multi-syllable adjectives."
Five months later I’m tremendously upset that fickle Google search has not as good as beating less good than 470 to 1 only. I swear it was 6000 to 1 when I first looked into it. Oops, it’s only 17 to 1 in the Ngram. But I include it below hoping it proves more constant. The first few pages of Google books search for less good than return almost only religion and philosophy books. They have more good too (my emphasis):