Can you explain a bit more why you want to do this please?

I'm writing a set of functions in C which perform various computations (for multiple reasons C is a better candidate here for this specific set of functions than the Mathematica language). I had initially started my work with LibraryLink, however, couldn't figure out how to return arbitrary lists (which datatype isn't defined at compile time); some functions may return Real32Lists or Integer32Lists or else, it greatly varies on the arguments being passed as input. Likewise, the input(s) should be arbitrary, meaning those functions may be called with either Real32Lists or Integer32Lists or else. This problem went away when using "Manual" on WSTP; so I've used WSTP since. I intend to add Arrays at some point (for input/output), but only limiting the scope to Lists for simplicity in this thread.

With this being said, I will show an example of a function function1 takes two arguments, one string, one list (of arbitrary type). function1 then performs some form of computation on the arguments, and either returns something (likely a List or an Array, or else or nothing). Even if it doesn't returns anything, it may still have some data allocated in memory that another function might use to "pursue computation" if I may say.

Let me know if that makes sense, thanks for looking.

While conceptually a List is just another expression with head List and arbitrary elements, the implementation uses more efficient representations (packed array) when all elements are either machine reals or machine integers. This representation is maintained when sending the array through a MathLink connection. In principle, you can (1) detect if there is a packed array on the link (2) determine its type (3) use the correct Get function to retrieve it.

Unfortunately, how to do this is not documented. Lots of things about MathLink are not very well documented. There is a question about this on M.SE: https://mathematica.stackexchange.com/q/180706/12

I would not recommend trying to do this, unless you have a very good reason to do so (e.g. you do not know at all what expression you are receiving on the link). Instead, you can try to determine the type of the array in Mathematica code, and either pass in the type in some way (some encoding of your choice) to the C functions, so that function knows what to get, or just use two different functions (what you were trying to avoid).

If you do this anyway, LibraryLink will give you much better performance: https://mathematica.stackexchange.com/q/91887/12 With LibraryLink, having two functions will not be avoidable.

Note that by using LibraryLink you will not lost almost anything because optionally you can still use MathLink-based passing.

To determine the array type in Mathematica, use Developer`PackedArrayQ (see 2nd argument). To determine if a non-packed array is suitable for passing to your function (i.e. if types are homogeneous, if they fit in machine numbers, etc.) you can first try to pack it using Developer`ToPackedArray.

All that said, if you all wanted was to save a bit of memory, then just don't specialize the functions to integer/real. It will not save memory at all. If you care about performance a lot, just use LibraryLink.

Let me also recommend my LTemplate package with the caveat that you should get familiar with plain LibraryLink before starting to use it. LTemplate is most useful if you want to use managed library expressions, i.e. if you want to store some sort of data in C and manipulate it from Mathematica. I use it for my IGraph/M package, where I need to store graphs in C and manipulate them repeatedly.

I hope this information will help you make a good decision.

What I mean is that I want a ArgumentType of "Manual". Based on that I can WSCheckFunction() that the input is a "List" (this is what I want); but how can I find its datatype, and access each element, so I can parse it efficiently?

Why is just using reals not sufficient? Integer values can be stored in doubles.

uses twice as much memory

If yes, why are you using MathLink and not LibraryLink (which has much better data passing performance)?

Haven't found how to ReturnType "Manual" with LibraryLink, that is, I don't know the output of the function until it's run; I am not sure if LibraryLink can have a ReturnType as Manual like WSTP?

Can you explain a bit more why you want to do this please? Of course, this is a reasonable question, but the situation is a bit more complicated than you may be aware. The best solution will depend on what you are trying to achieve.

Why is just using reals not sufficient? Integer values can be stored in doubles.

Is this about performance? If yes, why are you using MathLink and not LibraryLink (which has much better data passing performance)?