Suggestions for lowering mother's bill

My mother has the one gig Fios service with TV and landline phone.  She has the G1100 router and several extenders. I'd like to lower her bill and eliminate wifi dead zones. 

1. Can I buy a G1100 router on eBay and sub it in so she doesn't have to pay the rental fee?

2. Can I install a mesh wifi like I have at my house? She currently has, I believe, three extenders but there are still serious dead zones. The Verizon extenders seem to run over the coaxial cable so I'm thinking they can be placed only where she has existing coax cable. If I were to buy a wifi mesh system, I could place the units wherever there is an outlet, which would be a major improvement. It would also eliminate the rental fee. 

3. Am I able to install the Verizon router anywhere she has coax cable? It's currently on the far side of the house and I'd like it more centrally located. 

4. She uses internet only for web browsing, email and occasional streaming. Does 1 gig seem like more than she needs?

Thank you in advance for any insights. I'm not a tech-savvy person. Let me know if any of this sounds too ambitious for my skill level. 

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