I've lived here for nearly 5 years. Can they take the [town]home away from me if my mom goes into a nursing home?

If you don't legally own your mother's home (the deed in your name and for longer than five years) and Medicaid is paying for her to be in a care facility, they will expect repayment because she owns an asset (her home). The town has nothing to do with it. A nursing home doesn't either. They lead people to think they have a right to property, but they don't. Medicaid would be the one paying and the one who gets repaid when assets get sold and liquidated.
Watch out for those state-sponsored family caregiver programs too. Yes, a family caregiver can get paid by the state to care for an elderly loved one. They claim an estate to be paid back whatever they pay out though. Same applies for agency-employed homecare aides that are paid for by Medicaid. Believe me, nothing is free for a person if they have assets that are unprotected or still in their names.
As for loss of your husband's income. Medicaid is reasonable. Because you are his legal spouse, you will be left with enough to live on. You should buy a small place though. As the spouse, you would be allowed to remain in the home and Medicaid will consider it a protected asset. Unless you go to sell it and then they will expect your husband's half to be paid back to them.

I was told by a Medicaid caseworker the Will means nothing when a person is being supported by Medicaid for NH care. Her SS and any pension will be needed to offset the cost of her care. The Will means nothing because Medicaid will put a lien on the house when Mom passes. That lien will need to be satisfied if house is sold.

You could claim that you were Moms caregiver in those 5 yrs. Definitely you are a resident. But you may need to prove you can pay the bills and upkeep for the home to remain in it.

If the house is sold before Moms death, that is her money and needs to be used for her care. In no scenario do you split proceeds according to the Will when the person is alive. The Will only comes into effect when the person dies. The house must be sold at Market Value when Medicaid is or will be involved at some point. If Mom is not competent hopefully you have POA because without it you can't sell the house.

Moms home is considered an exempt asset until her passing. When she passes, its an asset that Medicaid can recover the money they put out on Mom.

The question is whether your mom will need Medicaid (and whether she'll qualify). They don't take away the home, they put a lien on it that needs to be satisfied when the house is sold. I would consult with an elder law/estate planning attorney and/or a Medicaid Planner for your state to get the best, most accurate guidance since Medicaid rules differ by state and this is a global forum.

If "they" is Medicaid, no you won't get evicted immediately should she go to a home, but Medicaid's share will have to be settled before the property title changes hands, like in a will. Which as you said will split the value of what remains.

That said, there is an ethical dilemma in placing a senior who doesn't want to leave her house so that you and family can live in it by yourselves. With your husband on home hospice, your mom may well ask why she has to be the one to leave the house, especially as she owns it.

And that's key.

As she owns it, and as she moved y'all in to presumably never put her in a home, it would follow that the husband go into an SNF with hospice services before she has to.

You cannot split according to the will until mom passes. It is not an inheritance yet.

You may be able to stay there if you provided mom medically necessary care, and documented, for a period of two years before she entered a nursing home. This would mean that mom would enter nursing home as self pay from savings until spent down, then apply for Medicaid.

See an elder law attorney for requirements in your state.