If you have the skill, time and resources, yes, you could create do all of the above.
How is up to you.
One approach is mapping movement in a limited environment to an unlimited virtual enviroment. Through what boils down to sensory trickery the player is contained within the limited area but still able to move where ever they like in the unlimited virtual one.
Another is to use a setup where a person remains static, such as a treadmill, and their actions are mapped to virtual ones.
You kind find out more about these techniques by using google, checking our the Oculus Rift development sites etc.