Columbia..the Jacobsen belt driven pump is excellent as this type of pump can also be run dry. Just be sure you carry a spare belt. We use this type of design for bilge, water & washdown and they have given us better service life than the more typical flo-jet type pumps. You can always swap out but why spend $100+ bucks when you don't need to.
The t-off to your manual foot pump is typical and lets you still get water out of your tank when your electric pump fails. A better arrangment is to T-off a hose with shutoff valve in it and then run that hose to the foot pump.
The check valve you mention may be a pressure valve to hold line pressure and stop the pump from constantly running. Is there an accumulator tank in the system?