Liquid Rocket Engines can be clustered together on a stage but their performance, weight and size largely decide and constrain the design of the launcher. Data on the newer smaller launcher engines are unavailable, as they're in commercial development. What are some of the design parameters that change with scale and how does this affect it's weight and performance? How could one scale down the values of the large old engines to approximate these smaller ones?
Fundamentally, a liquid rocket engine consists of two parts: the combustion chamber / nozzle; and the turbopumps.
Combustion chamber / nozzle
It is easier to scale a combustion chamber down than it is to scale it up. Getting the fuel and oxidizer to mix uniformly in a large engine is more difficult due to the larger distances involved. Large engines suffer from combustion instability. This can be solved by adding baffles to the injector plate, as was done in the F1 engines (7.77 MN thrust) that powered the Saturn V.
That said, developing such a large combustion chamber is a massive task and (with the exception of the F1A derivative at nearly 9MN thrust) no higher thrust combustion chamber / nozzle has ever been developed. The next largest combustion chamber is found on the RS68 (3.56MN thrust.)
The Soviets / Russians have a long history of making engines with 4 combustion chambers / nozzles in order to avoid both the combustion instability and to reduce tooling / development costs associated with large combustion chambers. The most powerful liquid rocket engine flown, the RD170 / RD171, uses this strategy. At 7.9MN thrust it's only marginally more powerful than the F1, but each of the four nozzles only produces a quarter of that thrust. From this engine are derived the RD180 with two combustion chambers, producing half the thrust, and the RD191 with one combustion chamber, producing a quarter of the thrust.
One issue with scaling down engines is that you get proportionally more heat loss which makes the engine less efficient. But the percentage heat loss on something as powerful as a rocket engine is minimal anyway. Although engine cooling is proportionally a bigger issue on small engines, simpler solutions may be used to avoid complexity. For example an ablative nozzle may be used in place of a more complex cooling system involving circulating fuel through channels in the nozzle.
All large engines have their turbopumps powered in the same way: by combustion of the same fuel / oxidizer mixture that is used in the combustion chamber, as this is the most efficient way. There are variations in how this is done. It may be done open cycle, where the turbopump combustor runs on a balanced* mixture of propellants and dumps the spent propellant overboard, or it may be done closed cycle, where the turbopump combustor runs on a fuel rich or oxidizer rich mixture, which is then fed to the combustion chamber for further burning.
Some small engines use the same method, but there are other possibilities.
For example, the RL-10 (110kN thrust) uses its hydrogen fuel to cool the nozzle, and sufficient energy is obtained from boiling the fuel in channels in the nozzle to run the entire turbopump set. This is possible for a small engine as the surface area to volume ratio is greater.
In general, the smaller the engine, the more challenging the design of the turbopump. This is because the pressure generated is proportional to the fluid density times the square of the velocity of the outside edge of the pump rotor, so the smaller the diameter of this component, the faster it has to spin to achieve the same pressure. The same rules apply for the turbine that drives the pump. This runs on hot gas which has a much lower density than fuel. This means designing a small, efficient turbine to run the turbopump is even more challenging. Rocket Lab avoided the problem of designing such a turbine altogether in their Rutherford engine (Thrust 22kN, the smallest kerosene listed on Wikipedia) by using an electric motor to drive the turbopump.
SpaceX's Kestrel engine (on the now retired Falcon 1) was simpler still, relying on pressurized propellant tanks. There is a weight penalty for this approach for the stronger tanks, so this would not be used on a large engine.
Thrusts used in this answer are from wikipedia and quoted for vacuum operation.
*(In practice turbopumps do not run on a perfectly balanced fuel/oxidizer mixture, even on open cycle engines, because the flame temperature would be too high for the turbine blades. They deliberately run fuel rich or oxidizer rich to lower the flame temperature.)