At the moment, very few casinos give you a sign up bonus just to play. The vast majority will give you a bonus for your first deposit. There are also sign up free rolls, but with such bonuses you always have to do (usually) quite a lot of wagering to be able to withdraw. In other words, the sign up bonus amount does not matter as you have little chance of a payout, so I advise you to use it as a bonus to test the casino.
That is correct, more on deposit bonus not the sign up bonus.
Because the sign up bonus can easily be abused by users, as you don't need to shell out money.
Usually, you will find this sign up bonus for a very new casino trying to attract players on their site.
Also, keep in mind that most bonuses have conditions that you need to meet, so check out those conditions first.