I sometimes hear pilots request "cancel speed restriction" in countrys like Australia, do they mean to cancel the 250knot restriction and accelerate to ECON climb speed?
Yes. Jets operate best at their ECON speed, so climbing (or descending) at 250KIAS is not desirable. If you're running late, then climbing faster than 250 will help. At some ports in Australia where there are two restrictions, 250 below 10,000ft and also 250 on the SID/STAR, if ATC cancel the SID or STAR (meaning that the SID/STAR speed restriction is also cancelled) you will often hear pilots ask for a "cancellation of the speed restriction below 10,000" as well, because otherwise that would still apply.