Say I have some problem, like I can't download apps, and I also can't connect to yahoo (totally made up), but I can connect to everything else. These two issues seems to be related, and they may or may not have the same root cause. Since I can't know ahead of time whether they will have the same or different answers, should I post them as one question or two?
Post one question at a time in your made up case.
I can't download apps, and I also can't connect to yahoo [..], but I can connect to everything else.
The first part would mostly deal with the issues specific to app store/market app you're using, say Google Play Store. Since you can connect to everything else, it implies that the problem is specific to app itself -- eligible and should be asked as a different question.
In this case, the market app you are using would be diagnosed for issues. Starting from the error code you may be having, like "Error -505", then to the device specifications, and so on.
In the second part, you can connect to everything but Yahoo!. The first thing that comes to mind is whether this is connection specific or not i.e. is the problem specific to mobile data or Wi-Fi or both (I'm ignoring other network interfaces here)?
If Wi-Fi specific, the troubleshooting would be trying other Wi-Fi and more based on details in question.
If Mobile data, then it may be a DNS issue, ISP blocking the request, and so on.
If both, then the users would suggest more troubleshooting (hint: a malware).
(I suggested hypothetical troubleshooting, and actual troubleshooting steps could vary wildly. Nonetheless, the issues are separate.)
As you can see, the problems are more or less independent here, so they should remain separated.
Now, this answer wouldn't really help if I don't give a general solution.
Take a look at this question: On Android, how can I disable Google Chrome's incognito mode?. It bloomed from its parent question when a user gave such suggestion: When you lock down a Lollipop device to disable Chrome's incognito mode, this creates an XML "restrictions file". What actual XML is inside the file?
You would notice that the parent question could accommodate the child question in very few lines, considering the context parent question already has. Yet, it was decided by the poster to ask it as a separate question with details enough to make it stand out. It was a good judgement because the parent question is quite long (a bit messy too).
In simpler terms, always prefer to ask separate questions. If you cannot, then try hard not to intertwine those issues. Write them into separate sections so that they are easy to follow. The users who would detect that they are separate issues would possibly leave a comment explaining the reasoning and the suggestion to ask it as a separate question.
The reason I said not to mix them is because you now would be saved from a tangled question once you attempt to separate those issues into separate questions.
Note: Always do search and research (specially on the main site) before asking such questions, because if any of the issue has been raised earlier, then you would get a lot of info to identify whether the issues should be separated or not.
E.g. If you do a simple search like this here, you would see Q/A that would make you realize that the issue "I can't download apps" is altogether specific to Play Store only in your made up case.
Also note that you can link your two questions (mentioning the "other one" as "maybe related"). -- suggested by Izzy.