SmartThings doesn’t actually use Wi-Fi at all. It is plugged in directly to the ethernet router, but that’s only so it can talk to the Internet and some LAN devices.
Most SmartThings devices use either zigbee or Z wave. Those are the radios that are in the smartthings hub. It’s easiest to just think of those as two separate networks as Z wave repeats only for Z wave and zigbee repeats only for zigbee.
It’s also important to note that Wi-Fi can drown out zigbee, so the stronger your Wi-Fi is, often the more difficulty your zigbee devices will have getting messages back to the hub. Z wave does not have this issue.
So your post actually breaks down into several different questions.
If you’re asking specifically about your Wi-Fi network, I’ll leave that to other people to answer. But it’s just standard stuff – – there’s nothing that involves SmartThings as far as Wi-Fi goes.
If you’re asking about how to build a strong network for zwave and zigbee devices, see the following thread. It should answer most of your questions. 