Pretty much everything we think of as 'crucifixion' comes as a result of what happens leading up to and including the execution of Jesus, but prior to this event crucifixion was a vague and nebulous activity. 'Crucifixion' covers a wide range of punishments arranged around the concept of 'suspension', and within the Roman context means roughly something along the lines of 'attaching someone to a vertical torture device'.

Part of the problem is that the literature is so vague about what it means to crucify. Julius Caesar's crucifixion of the Numidians simply says they were attached to a crux (in cruce...suffixit) which doesn't state what happens next. Sallust uses several words (crux, excruciere, cruiatus) and appears to use it as a severe form of torture but not necessarily attached to death - although he does record one instance of that, which might imply that not all crucifixions lead to death, and the same goes for Livy - sometimes it's explicitly connected to death but not always. The clearest example of someone being crucified for a time period and taken down would be Sopater - you can read the text here (sorry for the rubbish quality), but here he's taken down after an outcry from the people.

There is no defined thing called 'crucifixion' - it was a set of punishments that varied from locale to locale. It could be a punishment and it could be a punishment that led to death, but sometimes corpses were crucified, so being crucified didn't necessarily mean you were alive to begin with.

It was an extremely painful way to execute someone. You didn't die from the nails in your hands and feet, you died from suffocation due to the position of crucifixion not being conducive to breathing properly. At first those who were crucified would be able to stand (or support their weight) using their leg muscles and stay in a position that allowed breathing, but once their legs gave out to exhaustion, they would slowly die of suffocation. If the Romans were feeling generous that day, they would break your legs to spare you the time wasting leg exhaustion part. This is mentioned in the Bible. The guards are ordered to break Jesus's legs, but he had already died, so they didn't do it. I'm not using the Bible as a factual reference here, that's just a applicable example. Another fun fact about crucifixion was that if you were a Roman citizen you couldn't be crucified. This is why it is believed that when St. Paul (a Roman citizen) was killed he wasn't crucified, but instead beheaded.