Many things to do.

I like showing my island when someone visits me. I hope they to be fine with this. Anyway, today I must to do many things, like cleaning my house, for example.

I am writing this before I will go to my English class. Yesterday, I wrote a notebook and sent it to my teacher's email. I am learning to improve my vocabulary about looking after yourself myself, like keeping fit and beauty treatments, for example.

It is my last week of the course.

I hope to pass the final exam, because I would like to do the next English level.

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Many things to do.

This is good!I'm going to write suggestions for more fluent English! 

I like showing people around the Island when they visit me. ( "show you(him/them) around" is a common phrase) 

I hope they to be fine.I hope they will be fine.

("I hope they will be fine" is not what you want. Try:I hope they enjoy themselves, or I hope they will have a good time)

Anyway, today I must to do many things, like cleaning my house, for example.

"Need to" or "have to" is more common. We usually don't say "must"

I am writing this before I will go to my english class. Yesterday, I wrote a notebook and sent it to my teacher's email.

"notebook" is the name of the italki section, but is not used like this. I have a notebook, or I wrote in my notebook are correct!  

Try: Yesterday I wrote a: paragraph / journal entry / entry in my notebook

I am learning to improve my vocabulary about looking after yourself, like keeping fit and beauty treatments, for example.

"Keeping fit" and "beauty treatments" are not commonly used words. Try: fitness, working out, hygiene, self-care, hair and makeup 

It is my last week of the course.
I hope to pass the final exam, because I would like to do next English level. 

I would like to move on to the next English level. I would live to advance to the next English level. 

Good job!!