My take: 35 years ago, William and Delores were at the village with the church spire. They're attacked by William's BIL, and William kills him. Then Arnold (and maybe others) attempt to sort out the problem, and Delores kills Arnold. That area of the park is shut down, and the town is covered by sand, leaving just the spire sticking up & decaying.
No-one realizes that William killed his BIL, they think it was Delores. So William goes home, marries, and becomes a model citizen. Each year he returns to the park and reminds Delores of what she did (hence the screaming in the barn when he drags her in there). He ages, and becomes the MIB. Eventually, his wife kills herself. Even though William behaved impeccably, she always knew that he could be a killer.
This means that William/MIB is one of the key investors in the park.
Not sure about all the stuff to do with constellations and the information that the corporation are after - I suspect that those will be Season 2 explanations.
Possibly the gun and photo were buried by Delores' farm by William/MIB to see if it would jog her memory. Possibly her mother is a host version of his wife.