Yo man,
This is your third post about you friggin Amazon gift card. Enough already. Respect the sub.
Replacing or buying your own router is not going to help you game. You need a different method to connect, because if you could wire in with Ethernet, you would have already done so, and probably not be complaining.
People telling you to buy an Ethernet cable are on the right path, but if you really live in a house with 8 people, you won't get away with laying that cable across the floors.
Try Powerline Adapters. It uses your power outlets to form a wired connection to your current router. They have a bad reputation, but sometimes the work surprisingly well. Just keep in mind that gaming doesn't need a lot of speed, just good latency. Powerline can often give you much better latency than crowded WiFi with 8 people on it.
And guess what? They are $49.99:
https://www.amazon.com/Powerline-Ethernet-Adapter-Extender-TP-Link/dp/B084CZMYNM/
Just return them if they aren't good for your room.
Use free shipping from Amazon.
Scenario 2 is more accurate for BOTH cases, but not because you used a switch. Scenario 1 is false.
It's the ISP provided speed that is the limited resource. You have 100 Mbps of Internet service, which can be consumed by any single connection. If multiple connections want to use Internet, that speed gets split up between all the devices trying to use it simultaneously.
It does not have to be in equal pieces. If one connection only wants 20 Mbps of Internet, another connection can use the other 80 Mbps remaining.
Using a switch does not affect the consumption of Internet from devices unless the switch port speed itself is lower than your maximum ISP speed. This isn't true in your example.