Interiors are really three main things, assuming we are just reupholstering, gluing, painting stuff, repairing plastics (plastics in airplanes are bad and it is time consuming to repair and about as time consuming to replace)
https://www.planeplastics.com/
#1 Placards - They must be there, if missing they must be replaced. An A&P should know which references to research to ensure they are there. Could be simple stickers or silkscreen painted on.
#2 Flammability - Applies to all in some way. The newer the aircraft, the more specific it is and more substantiation is expected. Typically its not much different than what automotive manufacturers do nowadays. There are companies that offer services to burn test and certify materials. Some of them put up free educational-type reading materials to help those interested in services. They are usually very helpful in determining what you need.
#3 Crashworthiness - This applies to aircraft
certified (not necessarily built) about 1988 or later. These seats were tested with crash test dummies and loads on the spine were measured to meet specific regulation. This means that the seat cushions are a specific design and any new cushion must meet those requirements. To get around designing them yourself and getting those approved you should be able to buy FAA approved cushions and then you can sew and install dress cover using materials that are burn tested.
If a guy pulls up in 1948 Luscombe 8A, 1968 Cessna, 1977 Piper, there is a pretty good chance that only the very basic flammability (mentioned in previous posts) and no specific crashworthiness regulation apply.
If you are certain you want to expand into aircraft, maybe you can offer service through an existing aircraft shop nearby. That would get you on the job and you can learn & go from there. More and more large shops are leasing/renting out spaces in their buildings to vendors that do things that the big shop doesn't want to do. (Example: jet windshields, at $20k a pop you can't afford to mess them up so they are almost always done by a windows dealer/vendor which is all they do)
Tip: One thing I absolutely hate about interior jobs is that it sure seems like some folks working on them have a tendency to drill new holes and add screws where they feel like it, those people should not be working on airplanes at all.
Weight is a very simple issue yet it gets ignored a lot, especially by owners doing their own interiors.