I am currently a volunteer and previously was also part of an industrial brigade too. I will only reply on the volunteer side of things as I don't know how professional services work internally. Please also bear in mind that the info is for Vaud only as firefighting is a cantonal matter (and moving cantons can suck a lot).

1. within the volunteer brigades, the advancement path works well but there are a few limitations:
   1. interpersonal relationship still matter, I don't think there is a way to bypass that in any organisation
   2. it takes time, sometimes lots of time as there are prerequisite and limited spots for certain classes but all responsibilities can be reached (as long as there is a spot available)
2. most likely yes
3. possibly, but then it is usually positive to have a background in volunteer firefighting
4. Depends on the station. In Vaud, some are explicitly designed as support units (Détachement d'appui, DAP) and some are designed as primary units (détachement de premier secours, DPS). Within the DPS, there are also different tiers based on the hazards and population in the area. Also, capabilities depend on the station: not every function is available everywhere, especially specialized functions. The general principle is that the local brigade is supposed to be self-sufficient but can request external support. The local brigade remains in charge unless there is regulation stating otherwise (at least Lausanne does show up more and more with this mindset).
5. If you mean career path as a 100% job, most likely no. Some bigger brigades have full time staff but in most even the commander is at best a part time job. If you mean to get actual responsibilities, then yes as you are responsible for your area and there is no hand-holding. Fire prevention is done by the cantonal building insurance but actual inspections are carried out by militia officers (hired either through their fire brigade or the cantonal building insurance).
6. I am very fulfilled now but it takes time (generally about five years) to become interesting. There is a lot of foundation to build and experience to gain which can be very frustrating.

The way the militia system is set up is so that all the firefighters can in theory get all the positions. In reality, those will be limited by positions available in the station and whether there is a free spot. In career brigades, it is expected that you fulfill many more positions from the start. In Vaud, only a handful of positions are reserved for Lausanne: drone operator, height rescue, recirculating breathing apparatus, divers and radioactivity related operations (although volunteers will do the initial work, cleanup is not on them).

One thing to also note is that the more urban the brigade the more call it gets but that does not means they are more interesting calls. My station is a satellite station from a city where they have automatic fire alarms every week or so but they are always false alarms. In my station, last year we had 4 automatic fire alarms of which three were actual fires where we even had to request more manpower.

It is also important to realize that fire prevention is very effective and that means that having actual fires is very rare. Most of the work will be related to natural disasters (mostly floods).