At its core,

[MadMojoMonkey]

How I see it is that science is a tool. With homo sapiens wielding it circa 2020, no, we most likely can not exhaustively and precisely quantify and measure those. Still, I'm sure we could make pretty good qualitative assessments on many issues, far better than what eg. religion does currently. It might take a long time to perfect it, but what scientific endeavor doesn't? Science totally can (=could) answer if not all, at least most moral questions.

Science is a tool to help us avoid being tricked into believing something foolish, even when the person trying to convince us of the foolish is our past self.
As such, science deals in phenomena which can be unequivocally confirmed by any observer, without nuance. The only way to ensure that this is the case is to deal in quantifiable measurements. The application of statistics allows us to compare disparate quantities and determine whether or not those differences are significant.

Without this property, science loses any robustness of predictive power.

Let's try it the other way around, which moral question can not be answered by science?

All of them. Morality and ethics relies on how individuals feel about various potential actions and outcomes. There is no objective right or wrong. Only what it preferred and what it not.

E.g. we like to believe that murder is wrong, and punishable. However, state-sanctioned life-taking (of fellow humans) is OK, so long as enough of us (12 on a jury) agree that it's OK to take the life, or 1 special guy (POTUS) says it's OK to go "over there" and kill a whole bunch of people.

If it wasn't all shades of gray, then there wouldn't be any reason for continued debate after all these millennia of study.

I believe there's more flavors of utilitarianism than there's of Ben & Jerry's, I'm not at all sure what I'd endorse, most likely some version of consequentialism. I'd be satisfied with just showing whatever we'd decide to go with is better than what we currently have.

You're kind of making my point. There is no objectively "right" moral framework which can be incontrovertibly demonstrated to be superior to others.

The whole point of ethics is that it is a muddy affair where no single decision is going to increase happiness and/or reduce misery for all parties involved. (Not that we've yet demonstrated that this is a morally upright goal of our decisions.)