My condolences for your loss. I'll address your concerns as you presented them...
Liver disease is just one differential diagnoses of many when peracute (sudden) death occurs in our pet birds. We do see beak softening and overgrowth when hepatic lipidosis ("fatty liver") is present but those changes aren't pathognomonic (specifically indicative) of liver disease.
You mustn't be blamed. Birds will mask their illness until they're gravely ill and can't do so any longer. This is a protective action as ill-acting birds in the wild will be attacked by other birds.
Yes, she could have died of starvation or, at least, of malnutrition. What had her diet consisted of please? Seeds should have composed less than 20% of her diet. A diet of mainly seed and nuts has excessive fat, carbohydrates, and phosphorus; marginal protein; adequate vitamin E, and are deficient in amino acids, calcium, available phosphorus, sodium, manganese, zinc, iron, vitamins A, D3 (necessary for efficient absorption of calcium), K, and B12, riboflavin, pantothenic acid, choline, and available niacin. Ideally, a balanced pelleted diet such as can be found here: www.harrisonsbirdfoods.com or here: www.lafeber.com/pet-birds should be fed as well as hard boiled egg yolk, pancakes and cornbread, the tops of fresh greens, dairy products such as yogurt and cheese, fresh fruits such as apples, pears, melon, kiwi, and berries, vegetables such as broccoli, carrots, beets, asparagus, cabbage, sweet potato, and squash, and even tiny pieces of meat.
I like the idea of getting him a mate and, yes, as mentioned above, pellets should be considered. It can be a challenge transitioning these birds from seed to pellets but here's a good site that explains how that might be done: http://www.harrisonsbirdfoods.com/using-our-foods/small-bird-conversion/
Please respond with further questions or concerns if you wish.