Yes, the Master MFG 12 Volt Diaphragm Pump 1 GPM is an on demand unit. Per the manufacturer it will shut off at 40PSI and then cut back on again once it drops back down below that once again.
This is really a question beyond of knowledge of the product as it is not an intended use of the Master MFG 12 Volt Diaphragm Pump 1GPM. It would be best to contact the manufacturer directly for the answers to your questions. Master MFG can be reached at 800-864-1649.
Master MFG 12 Volt Diaphragm Pump 1GPM has not had very many complaints as far as being noisy. We would recommend to first contact Master MFG 800-864-1649 for the best help trouble shooting this noise issue.
We apologize but do not have just the diaphragm portion of the Master MFG 12 Volt Diaphragm Pump 1GPM (EF1000-BOX) available. You may try reaching out to the manufacturer for troubleshooting your current pump, or for replacement parts. Master MFG can be reached by calling 800-864-1649.
We would recommend contacting Master MFG directly at 800-864-1649 for confirmation or additional technical information regarding the use of the Master MFG 12 Volt Diaphragm Pump 1GPM (EF1000-BOX) with a solar system. Unfortunately, we are not familiar with specific hookup qualifications or procedures that may be needed for this type of set up.