Just a minor note: the income of each settlement depends on what this settlement produces (farming, mining, trade) minus a percentage of the expenses of your faction that corresponds to the settlement's population. (that was not a very clear way to say it, was it? )
In other words, the fact that Rhodos has negative income does not mean that you are actually losing money from owning the province, it just reflects that at the start of the campaign Rhodos is more populous than Athenai or Sparte, so most of your army's upkeep, your generals' salaries etc are paid from the city's coffers, even if those units were not produced in Rhodos.

About your other concerns: Well, as others have pointed out before, playing as KH in the early stages you have to make good use of your generals' bodyguards (they reign supreme on the battlefield) to compensate for your lack of macedonian phalanxes. For example you can pin the phalanxes from the frond with your Epilektoi Hoplitai and flank them with whatever you have. Also use your higher mobility to create local numerical superiority. As for playing as the Makedonai... The team wanted you to make a strategic decision from the first turn: Do I defend my southern greek conquests or do I retreat to face Pyrrhos?