I have a somewhat vague recollection that you can pay an extra fee that will entitle you to the variations, combinations and/or permutations of the individual claims; if you add a language like that to a dependent claim, is that, in any way, valid, and creates a variation, combination and/or permeation claim of any preceding claims prior to such a claim using the above language?
It will depend upon the jurisdiction the patent application is in. Some jurisdictions let you do that without having to pay any additional fees, for example the EPO, most European jurisdictions, Brazil, etc. Some others let you do that to some extent, like China, where you can have multiple dependent claims but a multiple dependent claim cannot depend upon a multiple dependent claim (i.e. claim 4 is not acceptable: 3. The apparatus of any one of claims 1-2..., 4. The apparatus of any one of claims 1-3). And some others, like the US, require the payment of additional fees.
In a PCT, it all depends upon the International Searching Authority or the International Preliminary Examination Authority. The written opinion in the ISR or the IPER may include objections to multiple dependency if the Authority does not accept it, but you can sort that out in the national/regional phases.
The most important thing is that the different combinations must be enabled and supported by the description, otherwise it is irrelevant if you have to pay additional fees or not because you are not entitled to the protection of such combinations. If your original filing is in a jurisdiction where you are not allowed to have the definition you mention, or you do not want to pay additional fees, then it is wise to include claim-like clauses in the description. You can find some information about this in the Guidelines for Examination of the EPO.
Multiple dependencies are strongly discouraged in the U.S. Here they are thought of as potentially confusing. In much of the world they are thought of as a way to have more compact wording.
In the U.S. you can get the same claims by repetition.
Just saying "variations are possible" will not get you anything, the specific variation must be spelled out.