That sound your hearing sounds like your pump sucking air at the end of the cycle when the float drops down to it's terminal level. Also, while shutting down the impeller will be slowing, so water will no longer travel up the pipes, it will just slosh around and mix with whatever water is flowing back down the line between the pump and the check. If there's a way to adjust the float so that it shuts the pump off with the water at a slightly higher level, that should be eliminated.
Are you saying that you are always running your backup pump? It's there as a backup in case you lose electrical power. You'll definitely get constant noise if you've got water running through half the pipes in the house all day. It takes a decent amount of water for that venturi system to work, so you'd hear it. If the backup is running, turn it off.
third, I'm pretty sure you've got check valves. Those red handled valves look to me like combination ball valve / swing checks. (see here:
https://www.plumbingsupply.com/pvccheck.html). Also, I couldn't tell because you panned quickly, but where the pvc turns to the black (pvc?) there are two hose clamps. Are those just to join the pipes? Or is there a small section in there with a fitting? That could be a check as well.
I can't tell what's going on with the main sump, I see a valve on the far right line, is that the main discharge line? then there is a wye that goes back into the sump, what's going on there? why are there two lines coming out of your main sump?
To help answer some of your questions:The power required is determined by your specific flowrate and head requirement.
Look, there won't really be much of a difference in the motor sound between 1/4 or 1/2 horsepower. The velocity of the fluid may make some noise, sure, but I really can't see that you'll be able to change it enough that you'd notice. This system will make at least a little noise, it can't be helped. The bottom line is that you'll either have a large capacity pump which drains the system quickly, but then has numerous start/stops every day, or you'll have a smaller pump that runs a lot longer during each cycle, but has less start stop cycles. There's no way to significantly increase the amount of time between cycles
while the pump is off without making the sump larger. You could look into changing the high level switch point on the float switch so that the sump fills up more between each cycle, but if and by how much you can do this will depend on your specific pump and switch.Like I said, I think you've got them, but they should be close to the pump; I'd say at least a foot after the discharge of the pump.Buy a plastic one...but in all honesty the cast iron ones are designed like that for a reason. They're sub pumps, they're meant to work in water, a little rust is ok.