Love-hate Relationship with Nature

'Ello, it's Cello who's struggling to get back in the reviewing game.

Let's just jump in (I'm not one for flowing reviews, sorry)

Living near the forest, I cannot hear rustling of leaves.
What I hear when the sun claims the sky
is crawling echoing on the zinc roof.

This first verse has a ton of potential. You have a beautiful second line, but the first and third feel a bit bland. It might be handy to use this opportunity to pull in some more senses. Waking up is an experience that everyone has been through so it's a quick and easy way to pull the reader in. Mention the feeling you get when you hear the cawing, or if there's anything unique that you may see, hear, or physically feel. Scent is always a wonderful sense too. It often goes ignored, but scents really help to set a scene.

My mother grows a banana tree outside the house.
I do not like the sour fruit, but the monkeys do.

There are plenty of readers out there who aren't used to seeing things like banana trees and monkeys (one of those readers is me) and this is a great opportunity to really get them interested in the perspective you have to offer. Talk about the build of the trees or the sound of the monkeys. Again, more senses.
I'd also like to say that the first and second verse didn't feel very comfortable together. I'm not sure exactly what to suggest to fix this but playing around with the idea of starting this verse with an opinion would be a good place to start. You enter the poem with a very personal narration then jump to focusing on your mom and her actions. Something expressing how you feel about the outside where the trees are grown or how you feel about the practice of growing fruit/gardening would work quite well.

I cannot appreciate rain
when the ceiling’s white deepens in patches,
emphasizing the perforated roof.
They dropped unwelcoming tears
to the bowls I have prepared
with sighs.

The last line of this makes sense but doesn't feel especially comfortable. I'm know the feeling you're going for and I know there's a word for it, but I can't think of it for the life of me. 'Somberly' is all that's coming to mind it's not perfect. It would work if you chose to use it though. (I'm hoping that someone will read this review and think of the perfect word and comment it below)

The only good thing that comes out of rain
is the coolness.

There's a lot to expand on here. Why do you like the coolness? Do you keep inside when it's cool or hang out outside? How does it feel? Does it change how the world looks? Does it change your mood?

I do love it when I have to go across the descending garden,
careful not to slip and fall to the drain beside it.
I’d pluck a kaffir lime’s leave and go back to the kitchen
to drop it into Mum’s boiling curry

(Just wanted to say that I like that you used 'mum' and not 'my mum'. It makes it personal and flows very nicely.)

I really loved this poem. Keep up the great work!
-ChocolateCello