Linear motion with and without Friction Could we still use Newtonian mechanics in a frictionless world?
 A: Yes, we most definitely could.  In fact, in a frictionless world, the law of inertia (in the absence of external forces, objects in motion stay in uniform motion, and objects in rest stay at rest) would be even more apparent than it is in our world, and Newtonian mechanics would be that much clearer and more apparent.  
There is nothing in Newton's fundamental laws that requires friction to exist--it is just a particular example of a particular force.
A: Yes; in fact, the only difference you would see in your Newtonian analysis would be the absence of frictional force vectors (contact friction, drag, etc.) where they would previously have appeared.
In general, you can consider Newtonian Mechanics a useful model for "garden variety" dynamics problems so long as you aren't dealing with any extreme circumstances (objects traveling at a significant fraction of the speed of light, distances approaching the Planck length, etc.) that would require you to invoke either relativity or quantum mechanics.
