Re: spacecraft with Artificial Gravity?

Note: throughout this answer, I refer to "centrifugal force" and "Coriolis force". I assume you understand that these aren't real forces; however, they're very useful concepts anyway.

Regarding your first question, asking whether it's possible to use centrifugal "force" to provide artificial gravity on a spaceship: Yes, it certainly is possible! This is a wonderful old idea with a long history in the space exploration literature. Gerard O'Neill's "Island One" and the "Stanford Torus" are two space station designs which rotate to produce artificial gravity. Stanley Kubrick's adaptation of Arthur C. Clarke's story "2001" also has good examples.

However, no spacecraft to date has ever used this technique. Why? Basically, because centrifugal "force" isn't the only effect of rotation. Rotation also produces coriolis "forces". These forces cause moving objects to appear to be pushed sideways as they move: for example, a ball thrown "upward" in a rotating cylindrical space station would appear to curve to one side, and a ball thrown in the direction of rotation would tend to curve "downward". If you're standing in a quickly-rotating spacecraft, these forces act on your head whenever you turn it: in particular, they act on the fluid-filled canals in your inner ear which provide your sense of balance. Turning your head quickly in a rotating environment can confuse your sense of balance: it feels like your body and the floor are tilting when they're not. This quickly causes nausea and motion-sickness. These effects increase with higher rotation rate.

Several people have conducted long studies in rotating rooms on Earth to find out how fast a rotation humans could adapt to. Quoting one study:

In brief, at 1.0 rpm even highly susceptible subjects were symptom-free, or nearly so. At 3.0 rpm subjects experienced symptoms but were not significantly handicapped. At 5.4 rpm, only subjects with low susceptibility performed well and by the second day were almost free from symptoms. At 10 rpm, however, adaptation presented a challenging but interesting problem. Even pilots without a history of air sickness did not fully adapt in a period of twelve days.

So we need to spin the spacecraft slowly to keep people from throwing up. But to produce one Earth gravity (one "g") at a slow rotation rate, we need a very large space station, since

   gravity = omega^2 r

   omega = 2*pi*f

For 1 g at 1 rpm, we need a space station 900 meters in radius!! This is far larger than anything we could build today. If we decide we're satisfied with 1/3 g, and use only people with good "sea legs" so we can use 2 rpm, the space station can be as small as 75 meters -- still pretty huge. We need much more experience building things in space (and more reason to be there!) before we can start building such huge stations.

One way to avoid building huge structures is to build two small stations instead of one huge one, attach them together with a strong cable 2 km long, and spin them around each other like bolas. This has its own problems: what do you do if the cable breaks?

Re your second question: Yes, one can also produce "artificial gravity" by accelerating the spaceship. People in the spaceship will feel like they're "pushed backward" as the spaceship moves forward. There are no Coriolis forces or other side effects. Unfortunately, we can't build a rocket which can fire for more than 10 minutes or so at anything near 1 gravity. Our rockets either run out of fuel too fast or don't push hard enough. We'd need to design something like a nuclear-powered rocket to use this as an artificial gravity technique. But if we did, we could travel through the solar system amazingly quickly. A trip from Earth to Mars at an acceleration of one gravity might take just a day; if one could carry enough fuel, the nearest stars would be less than 10 years away.

Re your third question: there are amusement rides which use centrifugal "force" to create an artifical gravity. Since they're small and rotate quickly, they tend to make people sick, but some people find this entertaining. Two examples I've seen are the "loop trainer" and the "floor drop" rides.

In the "loop trainer", you sit in a little car attached by a pivot to a large wheel parallel to the ground. As the wheel spins faster, the cars swing out so that your head points toward the center of the wheel. Then the wheel tilts upward until it's like a Ferris wheel; the centrifugal force keeps your head pointed toward the center of the wheel, even at the top of the ride, so as you do loops, you're upside down at the top of the ride. I rode this at Knott's Berry Farm: it made me very, very sick.

In the "floor drop" ride, you enter a large cylindrical drum, and stand against the curved outside wall, which is padded. The drum starts turning, and you're pushed against the outside wall by the centrifugal force. Then, suddenly, the flat floor drops out from underneath you! The centrifugal force holds you against the padded wall. Some people are able to sit or stand up on the wall while it's spinning, but because you have to move your head to do so, it can make you horribly sick; also, you're at risk of falling a short distance when the spinning stops. There is (or used to be) one of these at Knott's Berry Farm as well: I didn't ride it because I was still sick from the Loop Trainer.

References:
The Architecture of Artifical-Gravity Environments for Long-Duration Space Habitation; a wonderful paper on artifical gravity.
Information on the centrifuge facility to be installed on the International Space Station. This is a very small centrifuge to test the effects of variable gravity on small animals.