Well, my synthesizer/keyboard is probably a lot older (supposedly more expensive though, since it still features touch response, has a pitch and modulation wheel, etc). Anyway, as long as it has a midi output port (which yours obviously has), it will work.
Please note that I do not use FL Studio myself, so I'm not really familiar with its workings.
1) I have no idea about this unfortunately, however, the default way to compose using an external keyboard is note by note (step mode). Quite likely, you have a record button somewhere that you need to press to record any stream that you play (which will probably then end up in the piano staff, as you describe it).
I don't know about FL, but when using live recording in Sibelius, you pretty much
have to edit some of the recording settings (quantization mostly), since its default resolution is so hilarioulsy high I doubt even an extremely skilled player could actually keep the tempo exactly enough to generate a clean sheet of notes. (I believe Sibelius resolution, at least, is staccato 512:th note triplets at the current tempo). So you might want to look up your recording settings dialog, if there is one. Also, if possible, you should lock the tempo for the track, otherwise it will guess at what tempo you are playing, which will of course fail unless you play straight mechanico.
2) You probably have to create new bars to record any longer.
3) Sorry, can't help you on that one. Check the recodring / midi in dialog, if there is one. Otherwise, it might be a limitation of the software.
4) Yes, that is step recording. You have to actually insert the rests as well.
5) If you have no velocity control, it will use a default value. Usually that is max, but I guess it could just as well be half of the maximum velocity or something. Drawing the notes by hand obviously has another default velocity. If you cannot edit the velocity of the notes themselves (this is one of the few major downsides to using Sibelius, by the way), then you should probably use a master channel yes, given that the velocity translates straightly to volume and nothing else. Otherwise I'm afraid you're in for some hard times.
But hey, composing something up on your keyboard (live) is only the first part; then in your mind translating it into specific notes is half of the fun (nah... probably just about 10 percent, tops), so you might just as well use the step sequencer. I agree that live playback of course would seem easier, but as said - without proper quantization, it might look (or even sound, should you apply inproper quantization) totally messed up. The only part where I tend to try to use it is in complicated sections, where certain notes are to be held down while others are not and the like.
Well, hope that helps at least some.
Otherwise, there's a fair number of FL users around here that might posess better knowledge on the matter.