Newton's First Law.
Stays at rest or in a state of uniform
motion.
In deep space virtually no forces act so the spacecraft moves as above.
If
there are forces you have to use Newton's SECOND Law.
The second part of the
question.
Newton's third law refers to action and reaction. However I like to think of it
as:
When a force acts on one body an equal and opposite force acts on another
body.
So what happens in deep space?
The best way to consider the
spacecraft here is to think about the conservation of momentum of the rocket and the
exhaust gases. The total momentum (if the spacecraft is stationary) before the engines are
fired is zero. This must also be the case after the engines are fired. The sum of the
momentum of the gases and the spacecraft must also be zero. The spacecraft goes one
way, the exhaust gases go the other.
As far as Newton's third law goes the gases
exert a force on the rocket and the rocket engine exert a force on the gases and so the
spacecraft moves forwards.