Terminology
Hello Original Question Poster
You use the terms High on Profile and Low on Profile, and seek advice for both situations.
Be sure to know the difference between the Profile as calculated by the FM(G)C and the "real" profile, that is, your altitude/speed combination in relation to your track miles to touchdown.
If you have tied the aircraft to the FM(G)C computed profile, then opening the speed window and increasing speed will indeed lead to Autothrust increasing thrust. (DESCEND mode in Airbus, VNAV PATH in Boeing).
If you are above the FM(G)C computed profile, but are not coupled to the path (OPEN DESCENT in Airbus or FL CH in Boeing), then increasing the speed in the open speed window will lead to a steeper dive, with thrust remaining in idle.
Whether the FM(G)C profile is identical to your real world profile, depends on what is in the FM(G)C legs data. Sometimes an arrival route will have an altitude restriction that is way above or below the ideal idle descent path towards the runway. Other times, the FM(G)C route is much longer or shorter than what you will get in real life from ATC, depending on the traffic situation.
In V/S mode, the vertical speed is primary, and is achieved via pitch control. Speed is then controlled by Autothrust. A/T cannot give less than idle, or more than (e.g.) climb thrust, so if you ask for enough vertical speed, A/T may not be able to keep the speed at the desired value.
Remember that all this info is given to you by the FMA's: the acronyms in their respective positions really mean something.
Finally, the devices are speedbrakes, not speedbreaks, a break is time off to have a cup of coffee in between lessons.