Welcome to OCF, Sab! Im very sorry to read what your father has been thru already! He is very lucky to have you helping him.
A mandibulectomy is a MAJOR operation!!! Ive been thru it myself and know how many struggle with their long recovery. Patients who have had this surgery after going thru radiation treatments will have a compromised ability to heal. Thats what I ran into among many other complications. A complete recovery for this very invasive procedure is 2 years. Even when I was 1 year out after having the surgery, I still had a long way to go before I needed to accept my current health being as good as it will ever get. But my case had complications and all kinds of things very different from most patients.
When discussing different patients histories and trying to make comparisons, it never is a truly accurate assessment. Everybody is different and no 2 people are ever the same theres just wayyyy too many things that arent the same like, age, other health conditions, availability of quality medical care, stage of cancer, exact location and size of a tumor, same intake, same height weight, living in the same general area, same marital status and allergies... I could go on and on listing things that make it impossible to ever get an accurate picture of a similar patients experiences.
Our site is made up of oral cancer (OC) patients/survivors and their caregivers. We do NOT have medical backgrounds, degrees, clinical patient experience, or extensive schooling learning about medical things. Our knowledge comes from first hand experiences of going thru some difficult situations and we pass along what we picked up along the way. That said its not really possible to know if your father will ever eat like he used to again or not. What one experiences another may not. Bets thing you can do to help your father is to keep in constant touch with his medical team and discuss anything that changes right away. Id also suggest you should read the main OCF site to learn more detailed info about OC. An educated caregiver is a very strong advocate for her patient

You may want to speak to his doctor and a dietitian about redoing the barium swallow test down the road. Most patients will recover and relearn to eat after most procedures. But, theres always an exception to every rule too. Ask the doc about high protein whey powder to increase your fathers daily protein intake. Protein helps to speed up healing so that may be a big help. It comes in powder form and is easily mixed with any liquid if your father gets his nutrition from a feeding tube he can still try the whey powder.
Wishing you and your father all the very best with his continued recovery!!!