I am struggling a bit with your grammar, no offense, but I'll try my best to answer.
An AIO (All-In One) liquid cooler IS better at cooling, assuming it's of good quality, compared to a tower cooler / air cooler.
But the rest is down to personal preferance and what you can actually fit in your PC case.
In your Pure Base 600, you can fit a 360mm radiator in the top, which is much better than any air cooler. The best air cooler (Noctua D15) is comparable to about a 280mm radiator.
The installation of an AIO is about the same as an air cooler, depending on model.
Replacing the case fans can be a bit more work, as each fan has a power cable that needs to be connected to the motherboard.
If the seller says each fan comes in a box, if I understood it right, they do, but...so does the AIO? I don't really understand what the seller is talking about here.
https://noctua.at/en/nh-u12a https://noctua.at/en/nf-a14-pwm As for the CPU max temperature, yeah, it shuts down at 105°C TO PROTECT ITSELF FROM PERMANENT DAMAGE!!
Yes, it technically can and will go up to 105ºC, but it's a really bad idea letting it get that hot. You don't want your CPU any hotter than 80°C max.
But in the end, it's all down to the user - if you're comfortable building your own PCs, I would install my own CPU-cooler and fans. If you don't want to do that, having a professional install an AIO for you is your best bet. But know that there are crappy AIOs out there, and they typically don't last more than 5-6 years before the pump dies.
With a tower air cooler, the CPU always has some cooling, and as I keep my PC running all the time, me personally am not risking it with an AIO.