You most definitely want to read your agreements and double check things.
You most definitely should NOT be using someone else's computer, period. It may be difficult to discover, but data and files do not disappear when you log off your account on someone else's computer.
I don't have real answers, but you having worked at your friend's house should not have an effect on them being able to get a job with Telus.
Two people in the same household (is on the same IP address via the same router) will be a no no.
There is a potential way around this, though. If you have a wifi router that you can access and configure via an app, it most likely can run a VPN server, which allows you to connect from your phone remotely to your router as if you were connected to it via wifi at home. Then you can tether to a computer to your phone and be working from 'home'. in terms of your IP address. This might be complicated-ish, but is a potential thing to consider, if you have this as an option.
(Note, this is NOT the same thing as using a VPN service like NordVPN or ExpressVPN
https://play.google.com/store/apps/details?id=arproductions.andrew.worklog
I track each task with this app. Has many other features like keeping track of wages. Easy to use. Free but I bought pro version bc I love it been using it for 8 months
Oh sorry I said yellow bc I bought the pro version this is the app https://play.google.com/store/apps/details?id=arproductions.andrew.worklog
You punch in and out of each task. It adds it up for you along with your wage and keeps track of beginning of work weeks. You just need to enter info into the settings once you first download
I use TopTracker to track my sessions. It's a free downloadable tool for freelancers to keep track of hourly or minute-by-minute work that syncs your hours to your profile. I've been using it over two years, it's been great, no spreadsheet keeping. Since it isn't a browser extension, and you can change the settings so that it does not take screenshots of your desktop, it shouldn't be against the NDA.
Check it out and see if it's something that would work well for you: https://www.toptal.com/tracker
I am quoting the standard email they sent everyone on the program. "On the Lionbridge Rating Program, applications such as virtual private networks (VPNs), non-standard browsers, browser extensions such as ad-blockers or 3rd party apps that have not been approved or endorsed by Lionbridge are strictly prohibited while connected to Lionbridge systems and working on rating tasks.
VPNs: Any VPN Any Virtual Workspaces, for example Amazon or Azure Any Anonymizer
Non-standard browsers: Any web browser except Chrome whilst working on tasks in the Raterhub
3rd Party Apps, for example: LBTimer Vysor Rateraide The Great Acceptor The Great Suspender"
Hope this helps.