As Hamas first attacked Israeli civilians first just a few days ago., the Israeli prime minister has threatened to retaliate against Hamas with unprecedented force

There are lots of ways to change this sentence to make it correct, this is just the way that seemed most evident to me. Because the sentence began with "As..." you need to connect the two points together in one sentence.

The Israeli prime minister has threatened would return Hamas with unprecedented retaliation.

I agree with the UK leader's words that there should be no balance on the two sides.

I'm not 100% sure what you mean here. Do you mean that we should have a balanced opinion about the two sides.

Now, the US president is in Israel, while Russian leader, Putin, is visiting China.

"While" is a connecting word, so must be placed in a sentence with two separate points. At the beginning of a sentence, you can use "Meanwhile..."

While Russian leader, Putin, is visiting China.

What are they planning to do, w? Will the new Cold War be turned into a Hot War between the West and the East?