First, to answer some of your questions:
You can almost always refuse a bonus but not if you have wagered with it. So if you get a bonus you do not want, DON'T PLAY, not even a single $. Email the casino and ask them to remove the bonus. Whne they have done so, you can play.
I know of no place where you can withdraw, say half the bonus after fulfilling half the wager-requirements. It's always a all or nothing affair.
Think of it this way: Say you take a bonus form a casino. In this case the casino wants you to wager x amounts of $ before they will let you withdraw that bonus (this is called the wager-requirements for the bonus). In other words, you have to do some work (that is, play at the casino) before you earn your pay (the bonus). It's difficult to say something that applies to all casinos. However, here are some rules that applies to most:
Microgaming:
Bonuses are sometimes credited automatically, sometimes you have claim them, either by email or a claim-form on the casino-website. Sometimes you can play BJ to earn the bonus but most times not. This is always specified in the casinos Terms and Conditions. At most Microgaming casinos you cannot make a withdrawel before you finish your work. So say your playing to earn the bonus and lose it halfway through leaving you with only your original deposit, the casino will not allow you to withdraw this money. You will have to keep 'working' (playing) until you have fulfilled the wgaer-requirements.
Cryptologic:
The bonus is added to your account automatically. You can almost always play BJ top earn the bonus. You are also able to withdraw your deposit anytime, though if you want to withdraw any winnings and the bonus you have to finish the wager-requirements.
Boss-casinos:
Again, the bonus is added automatically. You can play BJ to earn the bonus. You can withdraw your winnings and your deposit anytime but this means that the casino will take back the bonus. Alos, note that you lose your own money first. So if you deposit $50 and get a $50 bonus and lose $50, the $50 left in your account will be considered the bonus. And as such you cannot withdraw it before finishing the wager-requirements.
Playtech:
Most of the time the bonus can never be withdrawn, even after finishing wager-requirements.
RTG:
Don't play there.
And something that applies to all casinos: ALWAYS READ THE T&C CAREFULLY AND IF YOU HAVE ANY DOUBTS, ASK HERE OR EMAIL THE CASINO!!!
Specifically, you should look for:
1) Wager-requirements
2) Excluded games (games that cannot be played to earn the bonus).
Hope this helps you out