I am planning to install an open source OS (for ex. Ubuntu) to my Fujitsu Lifetime 753 notebook.
Now the question - are these 3 devices all compatible with Ubuntu?
As far as your router is concerned. Ethernet and Wifi is such a clearly defined that any will work.
Brother printers in general work well with Ubuntu but most don't just work out of the box and you will need to install suitable drivers for it.
A quick search of the Brother web site shows that this particular printer is supported and you can find the download here
The best way to test if your computer is compatible is to try it without installing from a USB stick or DVD. If all seems OK install. If not you can ask specific questions with any problems you have before committing to install.