First of all you should consider whether the technical feature you are referring to is necessary for the definition of your invention, maybe you can claim your invention without any such feature.
In the event that it should be part of the claimed subject-matter, you should try defining it in a generic way so that all the alternatives are encompassed. For this, you need to identify how the feature relates to the remaining features and the overall invention. Following your example, a button by itself is completely meaningless, so you need to know what is the purpose of the button within the invention that makes it relevant.
Once you have to answer to that question, one way of defining the feature in a generic way is by referring to the function that the technical feature provides and associate it with other feature that does something based on that function. For instance, say you have that feature A is a door, feature B is a button, and feature C is a control device. You do not want to limit yourself to a type of button (because it can be a mechanical button, a tactile sensor, a proximity detector, etc.), and what the button does is commanding the control device to open the door. Then you can claim a door system comprising a door and a control device, the control device being configured to open the door upon reception of an input signal.
Another way would be to define the feature for which there are so many options in a generic way, for example a means + function defining, or a function + device. In this case, you have to make sure you have some examples for said means or device in the description, otherwise the claim may be objected to under 35 USC 112 because it may not be clear what kind of means are those claimed. In this cases you would claim 'means for inputting a signal to the controller', 'user input means', 'user input device', etc. which would encompass any such means as long as it is clear what kind of means they are (the description is very important in this regard). If you simply define 'attaching means', but means are described in your specification, it cannot be determined whether a person could be holding two things together is encompassed by the claim, or glue is encompassed by the claim, or screws are encompassed by the claim, etc.
Concerning functional definitions, these US examination guidelines are very useful.
Bear in mind that the patent law of some countries do not accept definition of features by way of its function, therefore in these most probably you would have to limit your claim to the examples described, e.g. a button selected from: a proximity detector, a tactile sensor, etc. In some cases these countries only forbid the means + function definition, thus the feature + 'configured/adapted/programmed to' definition is acceptable.
Concerning your second question (in the last paragraph), unless I am not understanding it properly, you are mixing up two different things: patentability and infringement. You mention that C is novel and qualifies as an invention. Well, if it is novel, it still has to be inventive (or non-obvious) with respect to the prior art to qualify as an invention. You can get a patent for C if you meet the novelty and non-obviousness requirements, but you cannot lawfully practice your invention if there are active patents protecting B, B1, B2 because you would infringe this patent (or these patents). The patentee of B, B1, B2 may forbid you from using, selling, manufacturing, importing C as long as part thereof falls within the scope of the patent, so you would need a license from the patentee in order to practice your invention, or have a C without B, B1, B2 (and equivalents thereof that may be determined based on the Doctrine of Equivalents).