Why would it want to be everywhere and comprehend everything? Human actions are driven by emotions and feelings in an effort to avoid pain and derive pleasure, as much as possible. The desire to learn new things is no exception. If you don't provide needs and means for their satisfaction, your thinking machine will just sit where you leave it, in a state of self-contemplation (of sorts).
Because it's in our nature to learn and improve, therefore a sentient machine might want to do the same. Knowledge helps you survive and the need to survive is the most basic.
It is
our nature as you yourself said (for better survival), but why would a thinking machine possess the same qualities that a human has? My point is that your machine won't have any desires if you barely create self-awareness. It wouldn't care if it survived or not. I doubt that it would even understand the concept of life and death and, unless you provide it with memory, its own existence as such. You know that you didn't exist before having been born or conceived (in fact, before becoming conscious) only from external sources. Internally, there is no before you become conscious or after you cease to be.
I'd think that because I've never met any intelligent beings besides other humans. I assume that since both people and animals have these basic instincts an artificial brain might also form them.
In my view a self-aware robot would like to acquire basic knowledge, like what it is and where, why was it built and by whom.
The memories are a good point here. At the early stages the machine would probably be guided by its creator and share his life experience, which is another troubling aspect.
An intelligent machine would probably not only take pure facts and compare them, but draw its own conclusions, like a child.
In fact, you needn't have self-awareness in a machine to make it draw its own conclusions. Neuron networks are capable of doing just that, though they don't in the least possess consciousness. Thoughts can be effectively emulated in respect to what can be considered an end result, i.e. a conclusion.