Your router is very old. The 802.11b technology dates from 1999. A first step is to get a new router. If it was provided by your ISP they should update it, or you can get any good router and replace it. The Apple Airport Extreme is excellent, but there are also less expensive quality routers. The current standard is 802.11ac (2014). The difference is striking - your router is limited to 11 mbps; 802.11ac is 1 gbps (1,000 mbps). Yours has only one frequency band, the newest has 2.
SSID is just a more formal term for network name.
The Bluetooth is irrelevant. My household has 2 iPads, 2 iPhones, an Apple watch, 3 Macs, 2 TiVos, 3 Kindles and a TV audio distribution system that uses Bluetooth. All of the devices have WiFi on all the time, and the iPads, iPhones, Macs and TV sound have Bluetooth on all the time.
One thing you might try on the iPhone is Settings/General/Reset - Reset network settings. This will erase your WiFi password, but you won't lose anything else. But I suspect the problem is the age of your router, as the iPhone 6S has the latest version of WiFi, and your router is way out of date.