There are a long time no write yousee.

"long time no see" is often used even if you are not literally seeing someone, but "long time no write" could also be used.

I thought you wasere busy or you took a trip or something.

I would like to share what I did for a longduring this time with you.

I assume you mean what you did while you weren't in contact with the other person.

I want to tell you, I work very hard, day after day.

Not necessary to repeat

I listened to a story in English, I listenalso watched

Past tense

also another video.

I learn and I keepremember the vocabulary by heart. I write a lot.

I speak with myself and I look atin front of the mirror.

Sounds more natural, it is one activity that you do in a certain place, rather than two activities that you do separately.

I take careook your advice.

I 'm proud

I want to say you I'm ready to speak with on Skype one day, if you are available.

No need to repeat again.