Low cost home care or does anyone have information on health care workers through the VA or other facilities that will be low-cost or free?

Contact the VA or better yet contact your local Veterans Assistance Commission. They can get the paperwork started to determine how much the VA will be able to help.
there are varying degrees of "service connected disability" and the criteria is changing all the time.
the higher degree of service connected disability the more services he can qualify for.
And you can get paid for caring for him as well.

You can also reach out to the VA and see if he qualifies for any type of respite care or assistance. My FIL qualifies for a bath aide 3 times a week and I can't remember what all else, but they have done modifications to his home that have assisted with his mobility as well (stair lifts, bars, etc). They recently helped with several hours a day of respite care (we needed 24 hours a day and they paid for 6 hours a day, the rest was out of pocket). I think a lot depends on wartime vs peace time service etc, but I would definitely reach out and talk to a VA social worker and see if they are able to offer anything that would help. It won't cover everything but it might help give you a start in the right direction if he qualifies for anything. There are annual limits though, but at this point I'm sure anything would be helpful.

Your dad needs to apply for Medicaid and be admitted to a LTC facility that will accept a patient "Medicaid Pending".

Ask if the social worker at the currentb facility can assist you in identifying an appropriate facility, or if they themselves will accept him as a LTC patient