The R9 280 is 3GB, right?
Fortnite is okay regarding CPU optimization, but it’s not exactly great for Intel chips (not quite as bad as PUBG, but still), though it eats through VRAM and gets pretty demanding on high settings.
Check those games using GPU-Z to see what your GPU usage and VRAM usage look like while you're playing.
When you hit a drop, lower the settings or crash the game and check the graph to see where those two stood.
Massive FPS drops like the ones you're describing are usually caused by running out of VRAM or some specific in-game effects overloading the card.
Mess around with the settings; some of them are absolute killers for VRAM and overall graphics. Things like draw distance and certain fine details.
Anyway, for GTA V and Fortnite, I know that processor is actually fine even at 3.5GHz. It isn't exactly top-tier, but you shouldn't be seeing drops like that. If it is the CPU, it's likely due to specific settings rather than raw power.
My i7 920
@3 is basically the same as your FX, and it handles Fortnite and GTA V without much trouble. It gets some drops, but the worst it hits is somewhere in the 30s—it never dips below 30.
The R9 280 is plenty strong for 1080p. You should have decent performance if your settings are dialed in properly. My HD7850, which is significantly weaker than the R9 280, ran GTA V on medium settings just fine (around 50 FPS without major drops).
EDIT: Sorry, missed that you already tried low settings. 8GB of RAM should be enough, but check your RAM usage too.
The FX8320 should be able to push at least 4.0GHz near stock voltage, so it's worth the effort.
And keep an eye on HWmonitor while you're gaming to see if your CPU frequency is dropping.