Those aren't bad or uncomfortable questions. Having as much clarity as possible helps ensure plans are on track, need adjusting, etc. right? Some folks stress over questions like this, but I think it's important to ask them, and to provide context to the folks on the receiving end.
So, I think you ask these questions with a few basic rules:
(1) Don't send an email/message with a question like that without being clear about how urgent the response is
(2) Send the question or have the conversation during the course of a "normal" work-day - instead of in the middle of someone's night/etc.
(3) Keep the emotions out of the question, hopefully helping to keep them out of the response
(4) Just always think about what might be involved in answering the question. Are you needlessly grinding someone for an answer or do you really need it?
That last one really hits home for me. Was most recently in analytics/product at a large financial services company (insurance) and am now in a start-up. But I see a common thread across the two: senior folks sometimes asking for answers/work without spending much or any time thinking about the time the receiver will spend trying to figure out that answer/work.
You want stable operations with some slack for the cases something goes wrong, you don't want ops that are constantly under stress.
Having slack and not being stressed are important, but they have nothing to do with asking uncomfortable questions.
Stopping bothering me with damn fool questions would be a good start … ;-)
If you make people talk to you despite being uncomfortable - for example, because you are their manager - they will find a job where they are comfortable.
Potentially your business runs on destroying people. I don’t think that’s a reasonable way we want to run society.
The way /normal/ companies handle this is things like agile retrospectives - what went wrong, how can we fix it. Did we have enough people? How did /management/ fail /the people doing the work/?
If I answer “we would need X more people to get this done tomorrow instead of next week”, does that actually change anything, or do you just respond some nonsense about how you can’t afford that and we should just work harder? Basically: are /you/ willing to make sacrifices for /me/, or is it a one way street?