If I live in my grandma's house will it affect Medicaid?

At this point Medicaid is not involved. As long as you do not use any of Grandmoms money for bills or upkeep on the house, you should be OK. This means taxes too. Now she is in NH all her money goes to her care. If Medicaid is ever needed, they will see her money was only used for her care.

If Medicaid does get involved, you may not be able to remain in the house because you did not reside there at the time Gma was placed in care. Under Medicaid the house is an exempt asset.

I agree that talking to a Medicaid planner is a good idea.

Every state runs their Medicaid program independently, that's why it's dicey for you to ask for importance guidance on a global forum made up of non-professionals in the area in which you need the right advice. Contact a Medicaid Planner for your grandmother's state of residence and get accurate guidance on her behalf. How you manage her funds will be very important, especially if you are joint on an a bank account with her. Her being able to qualify may be delayed or denied if you do anything that appears as "gifting" (and Medicaid gets to decide what is gifting and how much they tolerate). Also, most states' Medicaid only pays for LTC, but some states will pay for AL. Many states' program has a 5-year financial look-back period on the app, some are 2.5 years. Medicaid doesn't "take" anyone's house but instead puts a lien on it that needs to be satisfied once it goes up for sale. So you see, there is a lot to know and a Planner will give you all the best guidance.

No. You moving into your grandmother's house and taking over the bills and the upkeep will only affect her getting Medicaid if she outlives her cash assets and is no longer able to private cash-pay for the nursing home.
At 100 years old is seems like a shame that your grandmother couldn't have been cared for at home. Her remaining money could have gone a lot farther.
Whatever you do, DO NOT allow the nursing home any access to her bank accounts. Whoever is the POA for her needs to INSIST on a written bill every month from the nursing home which should then be paid for with a cashier's check.
Don't put the cart before the horse here. At 100, your grandmother very likely will not outlive her cash assets. Move into the house. Don't let the nursing home intimidate you. They want everything liquidated so they can take it all at once. You do not have to go along with this, and remember Medicaid is an entirely different seperate entity from a nursing home. They are not one in the same. They have different rules than a nursing home and the people at Medicaid are far more reasonable and far less greedy than any nursing home.
Move into the house, and see what happens in year. Good luck.