Not quite. You can generally leave but must returned when summoned. You may have a interpol notice sent to your country if you refuse to come voluntarily.
Who pays for it and organises the visas and your work and stuff?
I guess you. Not the government.
The wonders of modern technology allow witnesses to be interviewed remotely. Many courts actually do that.
It sounds worse than it is. Every country has some version. The example I use is from MyCousinVinny where the witness/fiance tries to walk out of the courtroom and the judge orders the bailiff to grab her. That sort of arrest is a near-universal power of judges. It only starts looking evil once that power is extended outside the courtroom.