People have many many misconceptions about how things work in space so it's no surprise that such a question would come up.
As an aside I once had a lengthy discussion over the way flames work in space any where there is no such thing as convection in microgravity. It took me some considerable time to explain it to the person but I got there eventually.
Anyway, it is understandable that some people have questions such as these. We're a planet bound species and have had nothing in our evolutionary history to prepare us for the way things work in zero-gee or microgravity. So no wonder it's a bit of a mystery for many people.
Everything in microgravity happens the same way it does on Earth but without the gravitational component.
What does that mean ?
Well lets say you're on Earth and turning quickly around a corner in a car. You feel pulled to one side of the car, away from the corner. You're also being pulled down into your seat by gravity. You still feel down as being down but perhaps a bit off to the side because of your motion around the corner. If you had a glass of water in your hand you'd see that the surface is at an angle and not flat as it is when you're stopped. Thats' because you have a force pulling it down and simultaneously a force pulling it to the side away from the corner. Lets say these balance so the angle of the surface of the water is the sum of them both which means it will be equally puled by both forces so it'll be at 45 degrees.
Now do the same thing in space.
You turn the corner and you feel exactly the same force on you "pushing" you away from the corner. Now there's no gravity pulling you down but you are being "pulled" or "pushed" away from the corner. You are still feeling a force.
If you look at our glass of water before you start you'll see that it's actually a ball of water in the glass because its surface tension is pulling the water into a sphere. There's no gravity pulling it down. You're missing a force.
Now look again at the glass of water when you're going around the corner. You'll see that instead of being at a 45 degree angle, like it was on Earth it will all be pushed over to the side of the glass. Let's say you have a lid on the glass. You'll have all the water on one side of the glass and half of the bottom will be dry. All of the water is being pushed away from the corner. This is because there is only one force active at the moment. You have removed gravity by going up into space and falling at the same speed as gravity pulls you down which effectively negates gravity as a force. There are other effects but I'm glossing over them to keep it simple.
So on Earth we can see the the water, and you, experienced two forces. Gravity, which we get used to and forget it's there most of the time, and the force acting upon us when we go around the corner.
Now in space we have negated one of the forces. So we will only experience the forces upon us due to our motion around the corner.
We still feel that centrifugal/centripetal force acting upon us to push us and the water away from the corner we are turning around.
We still feel forces that are caused by our motion.
If we stop our motion by switching off the rocket engine then we're not applying any forces and we've negated gravity by falling (microgravity) so we don't experience any forces acting upon us, We're floating freely.
If we switch on the rocket engine again the craft will accelerate around us until it comes into contact with us floating there, and then we bash into the wall that is now the floor and we experience a force that feels very much like gravity. If the engine switches off that force goes away and we float about again. If the engine reverses the what was a moment ago the floor will become the ceiling. And we see the old ceiling coming towards us as if we're falling upwards from the old floor to the old ceiling. They have now become the new floor and the new ceiling. If you switch off the rocket engine again then we'll float, and if it goes back to forward thrust we can stand on the floor, which was the celing but used to be the floor in the first place.
So if you have a rocket that's moving fast enough to generate the equivalent force we could go somewhere else in space whilst all the time feeling like we were still on Earth. The gravitational force of the Earth is replaces by the motion of the rocket so you can stand up properly, and play tennis, and go to the toilet in a sensible manner.
The bottom line here is that we feel forces in space when we accelerate. Accelerating means that we're applying a force. So we feel that force. Just the same as we do on Earth but without the gravity bit.
