I am wondering if resource request questions should be on topic, especially when resources are hard to find. For example, I've been wondering if there are any resources in English to learn Solresol, as so far I haven't succeeded in finding anything but dead links. Should questions like that be acceptable here? Some such questions seem useful, but I understand it could be a slippery slope to broad requests that invite endless lists.
The whole idea of Stack Exchange is to be a storage of quality information.
Information almost never exist by its own. Instead, it is based on resources, references, and prior works.
Hence, it seems to be nearly impossible to make a storage for quality information without links and references.
Even despite the "link rot", data decay (becoming obsolete or overridden), and other natural processes associated with any references.
Therefore, resource requests should be on-topic and be a crucial part of any Stack Exchange site.
The other thing is that question containing resource requests should pass the usual Stack Exchange filters: not being too broad or opinion-based, demonstrate attempt to own research, clearly stating what's wrong with the links the OP has found him-/herself, etc.
In general yes, but if they aren't specific enough they may be closed as too broad.
For the situation you raised above, when you can't find anything but dead links, that definitely would be an acceptable question, because you know that at some time the resources existed, you just don't know where they can be found now.
There is some precedent for this on other Stack Exchange sites about languages. The main difference here seems to be that the quantity of potential questions in this category is significantly higher, since while other sites only deal with one language, we deal with many.
I think such resource requests would be as useful as they are on sites dedicated to a single language. However, clearly allowing any question of this type is a bad idea, as you mention; since there are so many conlangs, a "resources" question for each would quickly become overwhelming.
Unfortunately, I don't think there's a reasonable objective way to determine which languages "deserve" to have a post dedicated to tools for learning them. However, I think we can reasonably judge which conlangs posts like this are likely to work for by a few criteria:
lesser-known languages, such as someone's personal project that doesn't have any "fluent" or dedicated speakers, are unlikely to benefit from such a post, as the majority of the resources are likely to be in the same place: the author's documentation of the language
simple languages such as relexes or place-naming languages also probably wouldn't gain much either, since there's not really much to learn to begin with, and any relevant answers would simply be links to dictionaries
On the other hand, such resource requests would certainly work for widely spoken conlangs like Esperanto (although perhaps its dedicated site would be a better place), Klingon, or High Valyrian, for the same reasons that the various natural language sites have these posts. They could also be useful for well-known but sparsely-documented or -spoken conlangs such as Occidental / Interlingue, for which resources may be difficult to find.