ToBE #1 : Which is correct - "its" or "it's"?

Answer : Both.

Yes, both are correct, but in different contexts.

So, when to use "its" and when to use "it's"?

It's : The apostrophe (') in this case stands in for missing letter(s). It's is a short form of "It is" or "It has".
Examples:
It's a bright day => It is a bright day.
It's been a long time => It has been a long time.
It's common-sense! => It is common-sense!

Though not wrong, it is uncommon to see "it's" at the end of a sentence as in, "That is the way it's".

In general, 's would stand for "of something". "Arjun's pen" => "Pen of Arjun" or "Pen belonging to Arjun". Though similar, "It's" does not mean "belonging to it".
That distinction goes to ........

Its : Yes, its means "of it" or "belonging to it".
Examples:
I have a pen. Its colour is black.
That's my cat and these are its kittens. (Note that "That's" stands for "That is").