Can nonworking half of light set be removed?
In a way, this is kind of like asking, "Doctor, I got a sliver in my finger, what do I do" to which he replies, "get into the office immediately, we need to amputate at the shoulder or higher"

I'm just kidding :)

But YES, you can, however, you really should skip the operation. Pulling the sliver or repairing the fault is more economical, but time consuming. Light sets are so inexpensive today its often worth it to buy a new set.

I tend to keep a few laying around that I can use for spare bulbs. Many bulbs nowadays can blow and still allow the set to work, but this isn't entirely perfect. A bad bulb, or a poorly seated bulb, or a broken bulb lead, or a lead not centered well, or a wire pulled out of the socket is usually the culprit. You can bulb swap unknown bulbs 1 at a time with a single socket you know is working.

While you can rewire a set, you'd now have to tape it, and also ensure you arent increasing the voltage so much that you overpower the remaining bulbs and blow them too. 100 light sets are usually using bulbs for 100 light sets. Turn that into a 50 or 25, and the voltage goes up.

Not worth messing with,and if it is, its more useful to keep the set intact.

The 3 wire part is leading the hot and neutral to another section of the lights, so if it is a 100 set, it is already 50 and 50 :)

Decide if you want the outlet, measure it from end to end with an ohmmeter, and cut and repair the last socket with the outlet if being used, re measure everything before plugging it in, and be sure to keep hot hot, and neutral neutral.

Dont both attempting it if you arent able to do this.