This phase II trial tests the safety and effectiveness of preoperative immunotherapy with durvalumab and chemotherapy with cisplatin and gemcitabine with or without futibatinib targeted therapy in treating patients with intrahepatic cholangiocarcinoma that can be removed by surgery (resectable). Immunotherapy with monoclonal antibodies, such as durvalumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Cisplatin is in a class of medications known as platinum-containing compounds. It works by killing, stopping or slowing the growth of cancer cells. Gemcitabine is a chemotherapy drug that blocks the cells from making deoxyribonucleic acid (DNA) and may kill cancer cells. Futibatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving immunotherapy with durvalumab and chemotherapy with cisplatin and gemcitabine and/or targeted therapy with futibatinib before surgery may make the tumor smaller for resection and may help prevent the cancer from coming back. Patients whose molecular profiling test result show a genetic change called FGFR2 fusion, rearrangement, or activating mutation, receive immunotherapy, chemotherapy and targeted therapy while patients without a FGFR2 fusion, rearrangement, or activating mutation just receive immunotherapy and chemotherapy. Giving targeted therapy based on molecular profile test results prior to attempted resection for patients with intrahepatic cholangiocarcinoma that has a risk for either not being able to be removed or for coming back after it has been removed may help improve treatment outcomes in patients with resectable intrahepatic cholangiocarcinoma.