Welcome to the family, FlowerLover. We are a great family but one not everyone wants to be a part of. Matt is correct in that the fluid in his abdomen is called ascites and it is a sign that the liver is not working properly. The liver starts to get a hard and not process well so fluid/blood back up and then the clear part of the fluid in the blood leaks out into the abdomen. Normally the fluid is not infectious although once in awhile it will get that way from something else. Draining it is the only fix. They can put a permanent drain in and it can then be drained at home. As far as what he should eat, increasing his protein intake will help drawn some of the the fluid back into his blood.
Also watch closely for changes in his behavior. The liver cleans ammonia out of the body and if its not working properly then the ammonia builds up. It can cause changes in the brain which would manifest as a significant behavior changes often paranoid, call be hallucinating, agitated or some people get real lethargic and sleep a lot. If these start happening then I would get him to the ER.
One thing your husband could do is talk to his father about what his goals in life are now. Does he want to have everything do to prolong his life or is he just looking to love as comfortably as possible? I would recruit any other family members that are a part of this and have a family discussion so every one hears the same thing. If he wanting to fight then definitely a second or even third opinion. However if he wants to just be at home and be comfortable then it might be time to talk about hospice. They can keep him at home and comfortable. The sooner you can start that the better they can help.
As for mowing the lawn and overdoing it....that's a man thing. My husband was still trying to do things he shouldn't be doing even in the week before he passed. Your FIL is probably frustrated adn angry at the whole process.....and being a man makes it worse. He wants to stay busy and keep his normal life. I would say let him do it as long as he can.....yes, he is hurting and yes, he probably should let someone else do it but he still can. In the long run it probably won't matter much. You might offer to make some easy to fix meals for in the freezer. Then just wait for when they need help and rather than offer to help just do it....or hire a lawn service for them.
Sorry things are so rough. My husband battled this for two years and there were times I shook my head and grimaced as he tried to do something.....his fingers and hands hurt so bad when he got cold but he was still hanging Christmas lights.
Good luck and keep us posted.