..Although there was a tendency to put younger sons into these occupations, it wasn't unheard-of for all sons to "serve their country" in capacities like this. Some families saw it as a matter of family pride that every member should have a useful occupation.(The General himself seems to be of this opinion, anyway.) So I don't think there's any real way of telling whether the General had an older borther that died, or not.

It might be more fruitful to think about whether he 'needed' an occupation for financial reasons...or whether he was just so awful to live with that his parents sent him away as soon as possible!

As for managing the estate...I think he has a natural talent for organaisation and management..possibly too much talent in this direction! Since Captain Tilney, his son, may well have had very light duties, he could- and I emphasize "could" rather than "would"- be able to spend quite a lot of time at Northanger, even though we don't see that aspect in the book.