1- It's part of the System Annunciator System and located on the glareshield- if a warning light is on out of eyesight on the overhead panels or fire warning system, the Annunciator on the glareshield may illuminate red and advise what system has an alert in amber. Pressing cancels it and arms it for another warning. Pressing the Recall (ie the annunciator) will again bring up which system is giving an alert (in case you have forgotten).
2- We do it at 1000' AAL and call for 'VNav'. Clean speed is obviously above Flaps speed and it will command an acceleration to retract flaps expeditiously to initial en route climb speed whilst maintaining a steady climb.
3- No, follow 2. On the 737NG, when you program a SID, it should give appropriate speed targets- just follow the flight director commands and retract flaps. If there is a special climb requirement, you could call for 'Level Change Speed 210' or just 'Top Bug' to climb at a desired speed.
4- Seat Belts I should think.
5- The Flight System is the same as on the 747-400 and 777, and wonderful. It has all the information there you could possibly want. To begin with, maybe focus on only the important bits until you learn to absorb all it can tell you. It makes flying NDB and VOR approaches astonishingly accurate and far easier. Learn to use (and love) the Flight Path Vector. It makes flying level far easier. Having flown an NG, the thought of going back to stone-age 300-500s will have you waking up screaming! With the NG, the 737 seems to have leapfrogged Airboos!