Q: Is a basic IDEA of an expired/abondoned patent also be considered as an infringement? Irrespective of product's design ?

A: The basic idea behind the patent scheme is to advance the progress of the society. An inventor discloses his invention to the society for the benefit of the society, and in turn, the government grants a benefit to the inventor: a patent, which allows the inventor to keep others from practicing the invention. But the patent has an expiration date, after which anyone in the society can practice the invention.

Thus, a person cannot infringe on an expired or abandoned patents.

If you have an idea about a gadget with a single button used to call emergency services, and someone learns of that idea, they'll be able to make that gadget. You are entitled to nothing under that patent law. Ideas are not patentable.

If, instead, you have more than an idea, and you actually have an invention, but you did not file for a patent for it, and someone learns of the invention, they'll be able to make that gadget. You are entitled to nothing under that patent law.

If, instead, you have an invention, and you've received a patent for it, then you should be able to sue the infringer for damages.

If you have a patent for a gadget with one button, does someone making a gadget with three buttons infringe your patent? Maybe. On one hand, if the only difference is more buttons, but otherwise the gadget works the same way, then there would be infringement. The maker of the gadget can't get around your patent just by adding more buttons. On the other hand, if the gadget works differently, or the three buttons do something more than just a single button gadget, then there may not be infringement.