Keithngan162 :
does the router bandwidth have anything to do with connection stability when several devices are connected?
Technically yes.
This is called the "backplane bandwidth".
https://www.google.com/search?q=backplane+bandwidth
But for 99% of consumer routers the backplane bandwidth is high enough for normal data usage.
If you were to use more backplane bandwidth than available you may add latency to packets.
For instance if you had an 8 port switch and each port had a computer with a solid state drive and you started copying a 4 gigabyte movie from each one to every other one, creating about 98 gigabits (7 gigabits x 7 x 2) of traffic (if i did the math correctly), you would most likely exceed the backplane bandwidth of a consumer router/switch.
But this is an extreme situation that most people will not encounter unless they are explicitly trying to test the router/switch's limits.
In a more realistic scenario of 3 computers on a wired connection looking at youtube/netflix and 3 computers on wireless doing youtube and facebook you shouldn't see a slowdown due to backplane bandwidth, most likely from your maximum download rate from your ISP.