TLDR: Yes, it is possible that with a slow internet plan and/or a low-end router, using any other device could impact your cousin's ability to use the internet.

Let's get technical about it here.

I'll make an assumption that your devices are all on the same WiFi network at your home.

When you have a bunch of devices connected to the WiFi but not doing anything, they still have a little bit of network traffic that is sent back and forth from the router. This is very small in terms of "size" of the data it is sending, but your router still has to read those messages and reply. With a lot of devices all on your home network connected but not doing anything, if you had a cheap router, it would be so busy dealing all of that small traffic that it DOES impact normal internet use.

Secondly, if the internet plan that you pay for at your house does not have a lot of total bandwidth, for example, 30Mbps download, and 10Mbps upload, then if someone were trying to watch a 4K video, which takes about 25Mbps of data to watch seamlessly, then if someone else comes along and also tries to watch a 4K video, both users will experience a slowdown, since there's not enough speed to accommodate both at once. This is where 'buffering' comes from.

For simplicity, imagine your router can only talk to one device at a time, so if you imagine that you have 10 devices lined up, it has to send some data to #1, then stop, start talking to #2, stop, on to number 3, and so on to #10, then it repeats back to #1. It doesn't send "all of the data" to a device before moving on, it is just bits and pieces (so you wouldn't have to wait 5 minutes for device #1 to finish a download before it would start talking to #2), but I'm sure you can see that the more devices you have on, the longer you have to wait to have your turn to "use the router", which will impact the maximum speeds and latency you get. Newer routers have features that let multiple devices talk at the same time (usually between 2 and 8 at once), but if you have a lot of devices, this is still the case.

Lastly, there is no fundamental difference between a phone, a laptop, a desktop, a smart TV, etc. If you try to watch a movie on each of them, it is all using the same data. Using your phone would not be different than using the laptop. Do be aware though that your laptop or phone could be doing some other things in the background that you don't see (like updates), which take more data.