I shall begin my question with the remark that I am not tech savvy at all!
The problem is the following:
A cluster of computers (laptops, desktops, etc.) A, B, C, D... are all connected to the same router. Let's say my computer is computer A and I am a guest at big brother Bob's home, who owns the router and computers B, C, D...
Assuming Bob has no physical access to my computer but can access the other computers, is there a way to prevent Bob from knowing what I am doing on the internet, or even better, to completely hide from Bob that I used internet at all? (short of his contacting his ISP and demanding a report or something which would take a non-trivial amount of time and assuming I don't download anything or watch HD videos which could show up as a sudden spike of consumption)
When it comes to hiding the names of websites I visit and internet searches, according to some research it seems like Tor does a good job in hiding it completely, even if the ISP is contacted. However, can Bob determine quickly (i.e. without contacting his ISP, using some cmd dark arts) that computer A has connected to a Tor node at all without physically accessing computer A? (Let's say it's not in the cluster anymore when Bob does his checks)
According to further research it seems to be impossible to get the internet history of all connected devices to a router without access to the devices, but I am unsure and opinions seem to vary somewhat.
TL;DR I'm basically looking for a way to make my internet usage as inconspicuous as possible during a very specific time period when indirectly connected to other computers via a router I don't own, is using Tor the best thing I can do in this situation to maximize privacy?