A few months ago, I started seeing these errors on my computer

What I did was replace the old SATA cables with new ones and the errors stopped popping up.

However today the exact same error messages were shown when my computer crashed while I was doing something important. I was able to see these errors when I switched to tty1.

Now I'm pretty sure, that it isn't my cable's fault as it is only 2-3 weeks old. What I did was to disable NCQ by typing in my file and BOY it worked like a charm. However, I'm a little bit concerned that it might have a bad effect on my computer because Wikipedia states NCQ like this:

This(NCQ) can reduce the amount of unnecessary drive head movement, resulting in increased performance (and slightly decreased wear of the drive) for workloads where multiple simultaneous read/write requests are outstanding, most often occurring in server-type applications.

Will disabling NCQ have a bad effect on my computer overall?

You probably did the right thing. The drive scheduler already reorders I/Os to minimize head motion. The net effect is slightly worse performance since you can't overlap commands. The problem is that drive manufacturers aren't testing on Linux (or at least not fixing bugs only found on Linux). Some drives work well with NCQ, but I've seen some with problems.

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