1 Yes, it's possible to light a room with LED light strips. Lots of people do it. But it requires doing your homework. If you are impatient and fly past your skills, the project will probably fail. There are a variety of ways to do it.
2 You'll need a significant amount of 12V or 24V power (24V means half the current, which greatly improves the situation with voltage drop and fading). You will probably want dimmers and amplifiers. And appropriate wiring.
3 Given that this will be your primary light, you should place importance on CRI aka Color Rendering Index. If you remember green fluorescent and some CFLs and very early LEDs, that thing that made them look awful was bad CRI. Hold out for 80+ CRI preferably 90 CRI.
You should also be thinking about color temperature. 4000K is similar to fluorescents in an office. Old incandescents are 2700K. 5000K is similar to daylight and 6500K is a cloudy day. You don't want colors that are too blue in a bedroom in the evening, because they will make it hard to sleep. If you just buy random LED strips and don't pay attention, you will probably get 5100K, which will be pretty blue. LEDs naturally make blue light and use phosphors to convert it to other colors, so they like to sell you the more blue LEDs because they require less phosphor and are therefore cheaper.
RGB or RGBW lights let you dial in any color temperature you want, including some insane ones, but the CRI is fairly poor. I'm not sure I'd want to use RGB as primary lighting.
4 The product bundle you linked is a complicated bundle of products, including an LED strip, a smart WiFi based controller (RGBW dimmer), and a power supply. You probably don't want to use that. If you want control via WiFi or Alexa, then look for a-la-carte controllers or dimmers that do that.
Keep in mind that the electrical and building codes require that you have a light in the room that responds to a physical switch in the usual location. That can be a smart switch talking to a WiFi or Alexa type system, but it has to work when you push it.
All the wiring needs to be done consistent with NEC low-voltage rules. If your power is over 55 watts (which is actually a lot in LED), pay close attention to those rules.