When you fry fish or meat, does the interior fat stay inside or does it come out and the surface absorbs the cooking oil instead? My question applies to both deep frying and sauteing.

With boiling, grilling or roasting, fat will come out of the meat.  So much of the fat or oils in meat or fish will leave the meat.

Does this happen to fried foods too i.e. do most of the fats and oil come out of the meat and get diluted in the cooking oil?  Thereafter only a small amount of the now diluted fat and oil is reabsorbed back into the meat or does the saturated fats and fish oils not come out during frying?
Chemically, yes. Heat turns solid fat to liquid form once it reaches its liquid phase temperature. That's why meat turns dry and chewy once oil dissolve (unless it gets cooked long enough the meat or protein chain decomposed into stew). People seared meat in high heat or breaded meat in deep fry in relatively short time to shield both the juice and marble fat from excessive dissolving and evaporation.