Your calculation is correct, but 8 amps is 96W which would likely melt a 30mm wire (you have a fuse). Estimating that you wire is 34 gauge, I believe you should limit the current to about 2 amps.
The wire will increase about 6-10% in resistance as it heats to a red heat.
Yes, 30/1000 = 3/100 = 3% of 50Ω = 1.5Ω.
The resistance tempco of Nichrome is pretty low.
If this skinny wire is inside a 1/4" metal tube embedded in ceramic, or under water, it can dissipate quite a bit of power.