How can I fairly distribute water pressure and flow throughout my home?
Piping systems restrict the flow of water through them. Elbows, valves, joints, and straight pipe all inhibit flow. When all faucets are off so there is no water flowing, the pressure throughout your home plumbing system will be equal at all points.

When water begins flowing, the pressure throughout the system will no longer be equal. The pressure near the source (your pump) will be highest. The pressure measured right before the water exits the faucet will be the lowest. As the flow rate increases, the velocity of the water through the pipe increases. The speedy water flowing past the stationary pipe and fittings causes friction. The friction turns the water's kinetic energy into heat. We see this as a reduction in pressure as we measure farther and father from the pressure source.

We can reduce the friction effect by increasing the pipe diameter. As we increase the pipe diameter, we slow the water velocity. (side note: 'pi * r squared' says area is the square of diameter, so doubling the diameter makes a huge reduction in velocity.) Using a 3/4 inch pipe instead of a 1/2 inch pipe will reduce the friction losses because the water will be flowing much slower.

In practice, you should run larger pipes to supply multiple fixtures that will be running simultaneously.

If the piping system in place is too small, and assuming the system can withstand a higher pressure, you can increase the pressure. As stated, when there is no flow in the system, all points in the system will experience the higher pressure.

To achieve your goal of ~50 PSI at each fixture, you would then install a pressure regulator upstream of each fixture. The regulator will reduce the upstream pressure, and supply 50 PSI to each fixture, up to a limited flow rate.

In practice, installing pressure regulators throughout a home water system isn't usually the best idea. Home water systems are expected to operate without attention or maintenance for many years. The point-of-use fixtures (e.g. faucets, toilets) are visible, and failures are obvious. A regulator, with internal moving parts and an elastomeric diaphragm, are often not visible. If one fails in a way that it leaks, the failure could cause significant damage.

Another responder suggested adding one or more pressure tank (accumulator). An accumulator stores energy close to the point of use. When the system is idle, all points will be at 50 PSI. When you open a faucet, the water will be partly supplied by the piping system, and partly by the accumulator. If the faucet remains open, the accumulator will run out of energy. Quite suddenly, the flow at the faucet will reduce.

As soon as you close the faucet, water will continue flowing from the source (pump) to the accumulator, re-pressurizing the accumulator until its pressure is equal to the source pressure. At that point, water will stop flowing, and the pressure at all points in the system will again be equal.

In practice, an accumulator solves a problem for a remote bathroom fed by 1/2 in. piping. If a person flushes the toilet right before entering the shower, the accumulator will maintain the pressure to both the toilet fill valve and the shower. When the toilet finishes filling, the flow to the shower will be relatively unchanged.

Further in practice, modern shower valves include a pressure balancing device (or scald guard), which limits the flow of hot water if the flow of cold water is reduced. Search for 'pressure balancing' or 'thermostatic' shower valves.