I'm really eager to being fluent in English.. I'm really eager to be fluent in English..

or "I look forward to being fluent in English".

I am really eager to being fluent in English.. I am really eager to being fluent in English.

I am really eager to beingcome fluent in English... I am really eager to become fluent in English...

I believe theat being steady is the important thing in learning English. I believe that being steady is the important thing in learning English.

being steady/being consistent I think I'd say "when learning"

I believe the steadybeing regular/consistent is important thing in learning English. I believe being regular/consistent is important thing in learning English.

I believe the consisteadncy is an important thing in learning English. I believe consistency is an important thing in learning English.

"slow and steady" is also a phrase you could use here, but I think consistency is closer to your intended meaning.

I will try to write some senetences every day, even itf what I write is very short! I will try to write some sentences every day, even if what I write is very short!

I will try to write senetences every day even it isf they are very short! I will try to write sentences every day even if they are very short!