First one clarification: I am talking about Frontier, not Frontier First Encounters.
The power level stays the same, no matter what you do (there is no dynamic background simulation as in Elite Dangerous). You can still participate. After you get through the delivery mission grind you will see military assassinations start to pop up. There you are instructed to assassinate "double-crossing spies" or "corrupt government officials" for your chosen faction (Imps or Feds, choose a side but don't work for both as it can hinder your progress, however I never tested that statement). You could consider this as some form of privateering as you are destroying "enemy" ships. After a while you will get photograph missions. The time window on these can be very tight so you will need a fast ship with a large jump range. There you are asked to take pictures of military installations which are in enemy territory. There you will get to fight against enemy military craft.
In case you also try First Encounters, here is some First Encounters combat info:
Regarding fighting against multiple ships that issue was solved in First Encounters. There you will get attacked by multiple ships without having to fiddle with the stardreamer. Also, when playing First Encounters, as soon as combat starts your ship goes automatically in Engines Off mode (you can tell by looking at the left hand ship shaped console, if it switches to combat mode you are also in "Engines Off" mode).
That means you will have to use the Enter key to apply manual thrust and I strongly advise to do so immediately after the alarm sounds together with a radical change of course. Otherwise you will be a sitting duck and you get vaporized instantly. Combat in First Encounters is A LOT harder than in Frontier. The AI shoots better and fires missiles like crazy, most of them also being immune to ECM. I had several very intense fights there. The key is to always stay in motion, apply thrust, change your vector. Single out the ships with the higher powered lasers first (you can tell by laser beam color) and destroy them, then go for the other ships. Sometimes you will encounter mean Imperial Explorers with 100MW beams. Even one grazing hit will destroy you instantly in a medium sized ship. Save often.
If you want to try First Encounters I recommend the Direct 3D version which as improved graphics and runs in Windows. Look for FFED3D in Google.