Native American speaker here.
Sorry, these all sound unnatural to my ear.
It's me who is so generous that's bought you such a gift.
American: The construction sounds like the gift receiver has mistakenly thanked the wrong person for the gift, and the speaker is jealous of that attention. Hence,
"It was me that was so generous to buy you this gift!"
Now,
"It's I who am feeding your hamster now."
Again, sounds foreign, and like a case of mistaken identity. If you insist on using "I", I would say:
"It is I. I am feeding your hamster now."
I would never say "It is I who is...", I will always say "I am...".
"It's I who usually eat all the pizza."
Again, never "It is I", unless that is the complete sentence. So for example where that would work,
Commander: "Who is second in charge here?"
Harry: "It is I." (but more likely Harry would say, "I am.", as in "I am second in charge here.")
So, I'd write:
"I usually eat all the pizza."
Now,
But can I treat that me as the pronoun I, for example:
No. It is more like the pronoun "her" or "him".
For "Is it me who don't understand you?!"
I'd write
Is it me that doesn't understand you?!
You cannot write "me who do not", it is "me who does not". And even then, Americans will say "me that".
Which applies to the next one as well.
It's not me who am mending your roof up there.
I would say
It's not me that is mending your roof up there.