Solomon would have commanded his workers to do the building. Alternate translation: "which you are having your workers build" (See: [[rc://en/ta/man/translate/figs-metonymy]])
The word "walk" is a metaphor for "live" or "obey." Alternate translation: "continually obey all my statutes" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Possible meanings are 1) "carry out all of my laws" or 2) "treat the people whom you are ruling justly."
# keep all my commandments and walk in them
These two phrases mean basically the same thing and emphasize the importance of obeying God's commandments. AT "carefully obey all I tell you to do" (See: [[rc://en/ta/man/translate/figs-parallelism]])
# I will confirm my promise with you that I had made to David your father
"I will do everything I promised David your father that I would do for you"