You really should be looking at the instructions and the options reference that came with the zip download more closely. All the information you're looking for is there. But here's some stuff that might help...
There is a hideFlash configuration option with the default set to true. This will, as it says, hide flash on the host page before launching floatbox. The purpose of this is that often flash will remain displayed on top of all other content unless hidden. Whether flash stays on top or not depends on how the flash objects wmode parameter is set. If wmode is set to "opaque" or "transparent" then the flash is ok and remains in the doc flow - it does not need to be hidden. If wmode is set to the default value of "window" it will float above everything and will need to be hidden. On your site it looks like wmode is set ok and you can safely set floatbox's hideFlash parameter to false - but please do your own testing on this.
The speed of floatbox opening is set with the resizeDuration parameter. This is number between 0 and 10. 0 pops up instantly. 10 is a very slow animated resize. Values in between are various speeds. If you want fast, try setting resizeDuration to 3 for a starting test and fiddle with it from there until it's to your liking.
You may also want to play with the overlayFadeDuration parameter if you want to soften the sudden screen change when a link is clicked.
By the way, you can test parameters by passing them to your page in URL query strings. For example, you could say
http://mydomain.com/mypage.html?resizeDuration=3 and try different values quickly that way.
I see you're using v2.46. There's good reason to move to version 3. In your case, because of the animated closing of floatbox. Now whenever I see version 2's behaviour of instantly disappearing when close is clicked, I cringe a little bit. It's much nicer to have a fade out and resize down the same way it fades in and resizes up. That's a short-coming of version 2 that I regret letting go out. (If you are thinking of moving to V3, wait until you see V3.11 posted soon. It's got a couple of fixes in it that are worth having.)
Cheers...