At my last job, I inherited a relationship between my company and a large number of Ukrainian outsourcers (Softserve) that was suffering from this issue. Our people would lay out a general message of what we want to do in an email or ticket. The Ukrainians would read it and ask questions. Some of those questions would get answered, others would go unanswered, others would get ambiguous answers from members of the staff arguing about it. The outsourcers, having good initiative, would eventually give up on the questions and implement something, which then members of the team would gripe about because it "wasn't what they wanted." When I came on, my boss told me "Take a look at these Softserve guys, they're not delivering, I think maybe we just need to get rid of them, up to you." Once I investigated I replied "There's nothing wrong here that isn't our fault." Then I worked on turning that relationship around via communication and it was very successful. But many people don't know how to manage an outsourcing relationship of this sort.
Here are some reasons you may not be getting an answer, I hope they provide some insight into what an American tech company may be doing internally that seems odd to you.
The manager may simply be overwhelmed with email. I know I got to the point in that position (managing 4 teams, 30 outsourcers on top of American staff, a critical position with support and sales touchpoints) where I was getting about 300 emails a day (not counting automated stuff like ticket updates and alerts, then it was more like 800), and if a quick look at an email indicated to me that the right thing would probably happen without my intervention - it might not get answered. Prioritization has to be ruthless sometimes. He may not even see it, or he may see it and think "he'll figure it out" and is under the gun to do something else right then. Or, he has to go get more information or permission from somewhere else, causing a delay (and when there's a delay like that it incurs more risk that the chain will get broken somewhere and the email forgotten).
The manager may think they already gave an answer - in another email, or to a teammate of yours, or verbally on the standup call that morning, or to your management - and assumes that the matter is settled. I know that when I felt a question couldn't be answered with a yes/no but needed its frame discussed, especially with someone with not so great English skills, I'd sometimes talk to the outsourcer manager or tech lead and have them talk to the person. Or they were asking an overly technical question and I'd point at a local tech lead and say "You! Follow up with Anton and answer this question." As a manager, once you have passed "the ball" to anyone it's easy to see your plate as cleared of that issue even when that might not quite be the case.
They may be trying to get you to show initiative. It's hard being an outsourcer - some companies want to treat you like a field slave and you shouldn't do anything someone didn't explicitly ask you to and write a big spec up for. Others want you to be working alongside their American engineers and be free to innovate and full of initiative and all that. We were one of the latter, and we had to work with the engineers and their management a lot to say "hey, please don't tell them what to do, and don't assign tasks. We want them to pull tasks from the scrum of their own volition and we want to leverage their smarts by letting them make decisions." So we tried to discourage "Mother May I" questions in the interest of empowerment.
Pure communication issues - I'm not even going to call it language barrier, because it's happened between me and my local bosses too. They skim an email and assume it's just me telling them what's going on. Or the email was to multiple people and they're not assuming that an answer should come from them. Unless there's a big red blinking line saying "ANSWER REQUIRED FROM YOU - YES YOU, MR. SMITH" they may just be overlooking the call to action in the email. Assume for each level up in management above you that their reading level has regressed to a much lower level - middle school for front line managers, elementary school for upper managers, kindergarten for a CEO. Sad but true. Also remember they are working at a higher level - if you put a question in as say a comment on a ticket, something that all the technical folks would see, the manager may not be as hip deep in the tactical execution and not see it. (I know sometimes people would say "I put in a JIRA comment asking for your thoughts" and I'd say "I filter all that out to a folder because I get hundreds of ticket updates a day, reach out to me specifically if you need something")
Ways you can try to mitigate it.
Bypass Asking When Appropriate. Understand the degree to which they expect initiative and individual decisionmaking of you given their corporate culture, then execute under that line and don't ask questions if you don't really need to. Also, ask local tech leads/American tech leads etc/your local management questions that should probably go to them. In the B vs A case you cite, I would personally give guidance "Do the right thing, and just send an email saying 'I am doing B first because it's a prereq for A and A will get done on time' without asking it as a question." If they don't want you to make that change, they'll speak up, and you've removed a blocker for yourself and a task for them (mandatory answer). That's a win-win from a manager's point of view.
Use Non-Email Communication. Use chat, phone, etc. to follow up - I know it's a little intimidating because of the time zone and language barrier but a phone call can cut to the chase on a week-long email tennis match. Email is actually a terrible communication method to get unambiguous and timely answers to questions, despite its convenience. If you have regular calls or standups, surface your questions there as blockers. If you don't, suggest having one! A 9 AM CT Webex/G+ standup works well for most American/Ukrainian teams (except sometimes West Coasters).
Use Clear Email Communication. Make questions and to-dos clear in emails - the question and who you expect to answer it should be prominent. Put one question in an email - if you put multiple ones, or the questions are embedded in other explanatory text, they are likely to be overlooked. If you have to fit multiple thoughts in an email, use bullet points. Use colors/bold to make questions or people's names with to-dos stand out. Use subject lines that are clear, a [RESPONSE REQUIRED] or other similar designator in the subject will grab attention. Make answering easy for the manager and you're more likely to get an answer immediately. Follow up on unanswered questions (every 24 hours is fine); it's not rude to do so.
Here's an example of an email a manager's going to likely not see/ignore (pulled from my email archive).
To: 12 Team Members Including Manager A
Subject: Re: Search Alert: More than 0 results found for "Dev NPE or OOM
I noticed an issue of this message in the logs:
BIG MULTILINE LOG MESSAGE
and I think it means the app servers are restarting every four hours, maybe there is a bug or something. I think it could be a memory leak, last time we saw this on this other app it was blah blah please don't read this anymore... Maybe we should look at this instead of some other planned work.
From the manager's point of view it's a) not just to me, b) has some arcane subject line that's probably the techies nattering on about something. 50% chance to not read the email. If I have 5 spare seconds I read the email and, if I make it through the details, don't see a clear question and certainly not one addressed to me, and I move on. Now let's look at an email that will likely get me to read and respond.
To: Manager A
Cc: The Team
Subject: [RESPONSE REQUIRED] Stop work to address app server restarts
I discovered that the app servers are crashing and restarting about every four hours from our log alerts. This is a severe issue that affects customers intermittently.
Manager A, I propose I stop work on my sprint tasks to address this as an urgent incident. I spoke with Engineer Y and he agrees that is the right course of action, so both of us plan to work on this immediately. Is that acceptable?
First, you checked to confirm technical details with someone else before lighting me up. The [RESPONSE REQUIRED] and clear subject line draw me in, the bolded name and call to action lets me know what is required of me. And, there's a default course of action described, so if still I am unable to reply for some reason (caught in manager offsite where they yell at you if you're emailing!) I know what's going to happen.
To: Engineer X
Subject: Re: [RESPONSE REQUIRED] Stop work to address app server restarts
go as you propose
(or) have Engineer Y work on that, you finish out your sprint task
(or) i do not understand, let's have a call to discuss
(or) no, Engineer Z told me about that and it's been going on for months, finish what you're on and we'll get that in the next sprint
Sent from my iPhone
Hope that helps some. Not all managers are used to working with outsourcers, and even those that are fall victim to time pressure and expectations. He certainly does not have any personal problem with you, just one (or more) of these factors is causing him to not answer sometimes.
P.S. Slava Ukraini!