A Japanese poppy is cute flower.

A Japanese poppy is a cute flower.

I'm watching poppies every morning.

"I'm watching" is a current and immediate action.

No one cares for them during when they don't have not flowers.

Anyone can forget them during Summer, Fall and Winter.

I feel cheer up, when I see them.

"To feel" is a verb, and "To cheer up" is a verb. You only need one.

If you feel cheer up, I will be happy.

By the way, most Japanese call the flower a poppy, but the flower isn't a poppy, it's nagamihinageshi/ナガミヒナゲシ.

I know it, today. I learned it today.

It was surprising and happened this day, so it seems more like you learned it instead of only know about it for a day.

I was supprised.

I'm watching poppies every morning.

No one cares for them when they're not in bloom.

The other person's correction works too, just giving you a second option :P

Everyone forgets them during the summer, fall and winter.

You don't need to capitalize seasons. :D

However they always bloom every year in spring.

I feel get cheered up, when I see them.

I still feel that this sentence is a bit weird, maybe say "I am happy when I see them"

If it makes you happy you feel cheer up, I will be happy.

By the way, most Japanese call the flower a poppy, but the flower isn't a poppy, it's a nagamihinageshi/ナガミヒナゲシ.

I know it, today. I learned it today

I was surpprised.

"Surprise" seems like a word a lot of native English speakers get wrong too, so don't feel too bad :P. When saying it at least where I'm from you really don't hear the first R sound it's more like suh-prize when people say it, so it can be kind of confusing :P