Fiction or not, it is definitely not wrong to point out that Earth would be vastly different if humans were not here to "keep it running".

I, however, doubt:

However, as the global warming continues, iceberg from the different part of the world would start melting. Seawater level would rapidly increase and would cover the land until it totally vanished.

As, with the vanishing of all humans, all anthropogenic climate change would therefore cease. (If there will be non-anthropogenic climate change in this direction as well, then you might be right.)

The Earth might then just be subject to "natural" changes and nothing what we humans unintentionally advanced as nature is well enough in recovering when left undisturbed.