1) The govt. runs on a one-year "use or lose" appropriation cycle. An FMO job mostly involves keeping track of spending against that appropriation to ensure all the money gets spent by the end of the FY. Most create their own "cuff records" on spreadsheets or DIY databases for comparison and with official records with a lot of time spent tracking down things that show up in the official DB that there is no cuff record for. So it is more of an accounting function than financial management.
2) FS officers and specialists bid on assignments. Your first one will be domestic for orientation then after about a year you'll be able to bid on overseas jobs. Assignments are made by a panel. Expect to serve at small hardship posts at first.
3) The FMO reports to the Counselor for Admin who reports to the Dep. Chief of Mission (DCM) so it is a mid-level, not senior management position. But since the FMO keeps track of the money they tend to get more respect than other specialties like IT.
4) Upward mobility is subject to turn-over in your specialty. If entering at mid-level FS-03 it will be three promotion cycles before you have a chance to be promoted to FS-02. ERs written by supervisors are evaluated by promotion panels — as much on the writing skills of your boss than your abilities. But getting recommended for promotion means nothing if HR does not identify a "promotion opportunity" for that year. For example a panel might rank you #2 of of 4 people at your grade for promotion, but HR might only identify one or no promotion opportunities that year and you are SOL.
In the FS rank is in the person, not the job, and "stretch" assignments are common. That means getting assigned as an FS-03 to a FS-02 or FS-01 job but only getting paid at the FS-03 level. Taking stretch assignments does help to get selected and ranked high by the evaluation panels for promotion, but actually getting one is subject to HR identifying the opportunity.
I was recruited into the FS at the FS-03 level when I was 30, working the first 5 years under the old retirement system then switching to the new one so I could contribute 10% into the TSP 401k plan and get a 5% match. I did three overseas tours (totaling 11 years) during my 25 year career — the last 10 as FS-01 — and retired comfortably at age 55. That's the goal I focused on and what kept me from quitting several times during the first ten years.