Bear in mind as a lord getting deep into commerce and worrying over funds is seen as beneath them ( see freys) plus like all the debtors the crown owed he was prob getting some nice interest anyway on top of his already seemingly limitless wealth
1) traders are already comming into lannisport to sell all manner of items for gold or trade goods for westerlands metals etc ....increasing the westerlands military and merchant navy isnt gonna massively alter that . If was gonna go down that path investing in essosi buissness through the iron bank would prob be an easier and more productive shout
2)its the 2nd largest force and probably tied with the reach for best equiped and best % heavy cavalry etc . Tywin also added an elite loyal force of footsmen to protect lannisters after witnessing abductions and raised up house clegane to give him 2 of westeros best warriors.......cant do much better than that.
3) not many great lords do
4) theres very little lords would do but theres no indication its in any great need of it either
Jamies rage at someone attacking near casterly rock ( tyrions first wife) would strongly hint at a well patroled area where incidents of crime near the rock are rare.