Replaced my first power cord. Will I set the house on fire?

we don’t really know but if you have turned it on and it works without arcs and sparks. Then if you touch it you don’t get shocked you probably did a good job. Well now I see the first photo of the connections it looks a little short on the wrap around the screws I think the code book has an example of 66-75% wrap NEC exhibit 110.3 its for aluminum wire but copper should follow the same rules 2/3-3/4 wrap. I would not be afraid of using this but might try to get the wires a bit tighter around the screws but good first job.

You left the normal electricians mess according to my wife , When I was an apprentice my training supervisor said don’t wast your high dollar time picking up wire that’s for the clean up guy. But I try depending on the job,

Note I find with stranded wire a pre twist of counter clockwise helps keep it tighter.