I have noticed the majority of the SID's have a 220kt restriction at certain waypoints. Most likely to keep the turn radius to a minimum. Is this usually waived or do you have to stay in flaps 1 on a heavy takeoff in the 777 until past those respective waypoints?
Correct - the primary reason for the existence of speed limitations in the SID is to ensure that you can follow the required track. Separation between some of them is minimal (prime example left turns to RIKET off 12R DXB vs left to DARAX off 12 SHJ). If the RNP1 tracks are not flown accurately then separation cannot be assured.
Speed limitations are usually waived WHEN THEY CAN BE (no need to ask - Air Arabia!) and no, "climb unrestricted" does NOT lift the speed restriction for the aforementioned reasons.
Edited for non-working "quotes"!