What is the ruling on installing and maintaining mobile signal amplification networks, knowing that the waves emitted from them cause serious diseases? And is it obligatory to abandon this work due to the possibility of doubt in it, or would abandoning it lead to sin by leaving the field open to non-Muslims?

If it is proven that booster networks cause definite harm to people, then it is not permissible to work in their installation, due to the Prophet’s saying, peace and blessings be upon him: "There shall be no harm or reciprocating harm." As for what you mentioned about non-Muslims taking over the work, it has no bearing on this ruling. And what we know is that specialists differ regarding the harms caused by mobile phones, so there is still ambiguity in the matter.