"We need a fire."
Translation:Wir brauchen ein Feuer.
I think in this sentence "fire" is supposed to mean something like a campfire, so it's countable. A group trekking through the wilderness might light several fires: one in front of each tent.
I think the difference is made between fire as a "material" (hot stuff, plasma, whatever you like to call it) vs. fire as a specific mass of burning things (a campfire, a house on fire).
If someone needs fire as a "material" e.g. to light a cigarette, you'll use "fire" in an uncountable way: "He needs fire." / "Er braucht Feuer." ("Do you have a light?" = "Haben Sie Feuer?") In the same way you'd say, "He needs wood" / "Er braucht Holz" (as a material).
Similarly: "The first town house was destroyed by fire in 1567" / "Das erste Rathaus wurde 1567 durch Feuer zerstört", "Fire can be extinguished with water" / "Feuer kann mit Wasser gelöscht werden"
If you're talking about a specific fire ("a heap of burning things"), you'll say, "The fire destroyed the house" / "Das Feuer zerstörte das Haus", "Someone has to watch over the (camp)fire" / "Jemand muss das Feuer bewachen", "The fire went out" / "Das Feuer ist ausgegangen", ...
Note that the event of a fire is "der Brand" in German: "In 1567, the town hall was destroyed in a fire." = "Das Rathaus wurde 1567 durch einen / bei einem Brand zerstört."
No, "Feuer frei" means "permission to shoot". You hopefully never hear this, no matter which side of the fire you're on.
Nevertheless you cannot say "frei feuer". First of all it's Feuer as it is a noun. Then it is neuter, das Feuer, you need to put the adjective to neuter, too: (ein) freies Feuer. This sounds like a bushfire.
I don't think you'll still need this answer but someone might. In "Wir brauchen ein Feuer" the word "Feuer" is in the accusative case as it is the direct object. "A" or "an" with neuter nouns in the accusative case is "ein". With feminine nouns "a" or "an" is "eine" and with masculine nouns it is "einen". The "einen" form is the one that catches everyone's attention because it breaks the pattern.
The dative case is for the indirect object and for use with certain prepositions. In the dative "a" or "an" is "einem"/"einer"/"einem" for use with masculine/feminine/neuter nouns.