Your trader isn't doing any work because there are no good trades available in the sector. Find a sector where things that are produced also get consumed (Power Plant -> Wheat Farm -> Distillery, for example), or, if you believe the sector they are in fits that criteria, leave them alone and they will try again after a while (You can also reissue the command to get them to seek new traders immediately, as they will standby for some time before attempting to find another deal).
As your trader levels up, you will be able to increase the range in which they will seek deals, and when they reach level 8, they will be able to become Universe Traders (though their range for finding deals will still be limited, they will not feel obliged to stick around the same neighbourhood, and their trading may take them to any point in the galaxy where profitsss can be made).
You will need to reissue the sector trader command to get the option to increase the number of jumps in which they will seek deals.
It may be a good idea to leave them as sector traders with a big radius even after they've leveled up, as some parts of the universe are much more dangerous than the others (The area around Argon Prime, for example, is super safe, while Omicron Lyrae is close to many pirate and Xenon sectors).
P.S. the reason your automated traders sometimes loop through wares with "Buy x ware" orders is because that's how they assess available trades.