Can I hook up a Netgear R6700 Nighthawk AC1750 WiFi Router to my Netgear AC1750 Modem Router?

1. Is there anyway to check to see if the Router part of my Modem Router is still working OK?  My wife and I keep having problems with dropped mobile phone calls and no bars showing on our Galaxy Note mobile phones. However, when we go to church, all of the bars on our phones show active.

2. Can I disable the Router section of my C6300 and introduce a seperate Netgear or other Router? Is there a way to do this and is it difficult?  My wife has an office upstairs and my office is downstairs. We can both get access to the internet using my C6300. However, this is a slow process expecially when we go to various websites. I believe a more powerful/faster Router will eliminate this problem. Does anyone know if this will work? Thank you so much.