A Battlesmith Artificer in my campaign wants to have his steel defender basically "programmed" to perform various tasks, many of which involve acting on its own accord. Things like standing guard, acting as an alarm clock, searching for food or water and bringing it back, etc. The description of the steel defender really does not address this, it just says it "obeys your commands" and covers actions it can take in combat. Is it capable of understanding and performing "standing orders" like this?
Yes, in as far as its intelligence allows
The Steel Defender feature says:
Your tinkering has borne you a companion, a steel defender. It's friendly to you and your companions, and it obeys your commands. See its game statistics in the Steel Defender stat block, (...)
The only limitation on actions for the steel defender is in combat, as there is a paragraph that states:
In combat, the defender shares your initiative count, but it takes its turn immediately after yours. It can move and use its reaction on its own, but the only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take another action. That action can be one in its stat block or some other action. If you are incapacitated, the defender can take any action of its choice, not just Dodge.
There are no restrictions given for outside of combat, so outside of combat, the steel defender can do whatever a creature with its stat block could do.
In its case, it even is proficient in Perception, which would be useful to keep watch, and it understands the languages you speak.
It has an intelligence of only 4, like a very smart beast (a baboon or velociraptor; a mastiff or cat has 3), and that is probably the most limiting factor on the kinds of tasks you can ask it to do -- if it cannot understand the concept, it won't be able to carry out the task. However, the game does not have rules that specify what a creature of a given intelligence can or cannot understand so that will be up to you as a DM to determine.