You pretty much have answered your own questions
As the plane gets lighter you need less thrust to continue flying at constant speed and/or fly higher speed by maintaining constant thrust.
Having said that,
- the lighter the plane gets, the more efficient it is to fly at higher altitudes, so on long flight planes tend to do step climbs as they get lighter. Ideally, airplanes would fly a continuous climb (however small), but due to various reasons no one does it. The only airplane flown that way was the Concorde
- the lighter the plane gets, the more efficient it is to fly a bit slower, so plane tend to slow down as they burn fuel, by reducing thrust. The speed differences are very small.
How much thrust do you require at the end of a flight compared to the beginning, e.g. on a 2 hour narrowbody flight?
On a narrowbody flying a short sector the difference is very little, as the airplane typically burns around 10% (or less) of its weight.
OTOH on a wide body longhaul flight the fuel burn will be 20-40% percent of the plane’s initial weight, thus the thrust and fuel flow difference will be quite noticeable...