*I'm sleepy....I drank black tea instead of coffee. --------Is that worked?

Not sure what you mean by "is that worked?" but perhaps you could say "did it work?"

*Which one was your water again?

Fine

*What was your name again?
Fine

*I'll have an apple for my lunch. It's going to work.
Fine (although I'm not sure what you mean by "it's going to work" here)

*You haven't been eating enough lately.

Fine

*You've been studying hard lately.

Fine

*I've been doing on a diet this week.

*She has been avoiding him.
Fine

*You have a lot to do today, don't you?
Fine

*I'm going to be able to speak English fluently.

I think it is better to say:

I will be able to speak English fluently

Hope this was helpful

Best wishes

Shaun

Please correct me sentences.

(I am not completely sure what you mean, but you could try the following)

It will not matter that their nationalities are different

or

It will not matter that they have different nationalities

*It doesn't matter whether I have money or not.

This is fine.  You could also try:

It doesn't matter if I have any money or not

*I'm sorry if I'm bothering you

Fine

*I would might stay here until next April. I'm not sure......

*I was be able to enter the membership.

I was able to become a member

or you could say

I was able to join

*I'll be able to get a job because my friend introduced to me to the owner.

*I must be able to speak English if I want to apply the job.

I think it is better to say:

I need to speak English to apply for this job

*I've been able to speak English fluently lately.

Fine but it would probably be better to say

My English has improved lately

or

I have been able to speak English more fluenty lately


*I'll have to hand in my homework tomorrow.
I'm going to have to call my mom.

Fine

*I hope you will do well.

Fine

*Is this what you want?

Fine

*It seems to rain.

It seems like it's raining

*She seems angry because I ate her chocolate without asking.

Fine

* It's going to be a happy moment.

(Not sure exactly what you mean)

*You should have asked me. I could have helped you.

Fine

*You could have accepted the plan if you had had enough time.

Fine

*Why didn't you accept the plan? You could have had got a good opportunity.

*I'm starting to look like old.

*I'm getting bored to live here.

I'm getting bored living here

or

Living here is getting boring


*You'll eat only this? ----These are fine for me.

You will only eat this?

or

Is this all you are eating?

(These have different meanings and I am unsure which you mean)