Why did the Nazis fight so hard with the USSR so close? Why not just abandon the city to the Russians? Especially as they ended up destroying the city anyway.

The Vistula river is an important natural obstacle of Poland, there is no way that the Germans were letting the soviet increasing the size of their bridgehead freely.

It was also a matter of prestige, as a major european capital city it was important to keep Warsaw, especially in late 44 after the disasters in the summer. And it was also out of question to let the Polish win a victory over them by just retreating.

Why did the Poles eventually surrender when they were going to be executed anyway?

Although the repression was terrible in the first days, the german ended by keeping alive the uprisers which surrendered and gained the status of PoW.