Here's my take on this subject:
It's a fluid thing. It changes based on trends, and due to that it's hard to have a definite answer. For example, currently assassins are getting extremely strong not only due to the introduction of a new item (Else LeBlanc wouldn't be strong as well), but also because the champions who counter them are weaker due to other circumstances. Due to this, questions regarding Meta or "what's strong right now" should be avoided, unless expressely identifying a specific patch. This however also runs the risk of being opinion based, due to the fact that I can simply say "Katarina is the best thing in bronze". While there is some truth to that, Meta also shifts between tiers. In bronze, harder to play champions (Kalista, Orianna) are less common (and as such non-meta). Likewise champions who are countered easily like Yi aren't so common in high elo — meaning not only the question should be identified with the patch but also the elo it refers to, at least for objective questions such as "What are the Meta Champions in X Elo in patch y.zz?"
This is also something that changes often, simply because Meta is the trend of different strategies. However this is much less subjective. "How do I deal with Katarina" is extremely easy to answer and it's extremely on point: "You deny her from roaming, and you abuse the fact she is melee without CC" (obviously explaining what abuse is). Essentially, Strategy Questions can be answered based on the scenario presented, so these are definitely on topic.
This is the easiest aspect. "Who won EU LCS in 2015?". "What are the hidden taunts of Jhin against Tahm Kench"? These should be marked with the patch they are relevant to though, if the answer/question is no longer valid. "Who has more taunts in the game?" is a question that one month ago was answered with Tahm Kench, but now it's Jhin. In fact, Jhin's taunt towards Tahm Kench is exactly due to that fact.
"Who should I pick"
These are risky. They attract opinion based answers. However, as long as they are based on logic and facts they should be allowed. One example is "How to deal with Heimerdinger". This has the potential to have several different answers, but they are finite. Heimerdinger can be dealt by being able to do 'x'. Picking 'Y Champion' or buying 'Z Item' are slightly opinion based, however they only are such because there's more than one strategy which is valid. Essentially this kind of question must be scrutinized and only allowed if it's in one way or another answerable with concise information.
"Who is stronger, x or y?"
This should be allowed, but only as long as the question itself specifies the scenario. A Sona going in against a Galio midlane is more than likely going to suffer a lot of issues. However if she's facing him in a duo lane, the story is much, much different. Answers to this kind of question must be, once again, based on facts and the inherent Pros/Cons of the Champions involved.
Most questions can be weighed on their viability in one single step. "Is this question answerable with facts based on deduction from the different capabilities of the characters involved?". If so, it's quite likely a great question. If not it's most likely too broad or opinionated. Note that this is also valid for other constantly changing games who are balanced in imbalance, such as DOTA 2, Hearthstone, Yu-gi-oh, Magic: The Gathering, and so on.