How can I get Dad into a senior apt?

Call your local center for aging or senior center, ask to speak with their director, social worker, nurse, etc...one of these staffers will be able to counsel you and help you navigate all the services available and help you evaluate dads finances, financial assistance, veterans assistance, etc., even meals on wheels as suggested above. They can locate HUDR housing for seniors, etc. in the meantime, your sibs might also look into same in their area and maybe get dad involved so he goes to senior center in their area daily or gets some in home care support.

Council on Aging of Southwestern Ohio can help
175 Tri County Pkwy, Cincinnati, OH 45246
(513) 721-1025

How and where do I apply for the assisted programs in answer #1?

There are senior communities that have subsidized housing in many areas. Check to see if you have one around you. If your father's income is low enough, he could qualify for Section 8.

I wondered whose SS was higher -- your father's or your mother's. If your mother's was higher, did you check into him getting her SS, instead of his own?

Your county has a aging agency, it called many different names. They can help him apply for low cost housing, set him up with food stamps, etc