Heisenberg's corrections were good, i just wanted to add a couple things:

My first job

Today,is Sunday.
Today is Sunday. [no comma]

I don't need to work, [this sentence is fine, but i would connect it to the previous sentence: Today is Sunday, so I don't need to work.]

I have started to work for a new job about ten days as a Software Engineer,Although I'm not graduate from my college.
I have started (to work/working) for a new job about ten days ago as a Software Engineer, although I haven't graduate from my college. [if you say when something happens, you'll use the simple past (i started, not have started). If you left out "about ten days ago", then you could use the present perfect (have started) to emphasize that it was recent or that it's new information.]

there is one day to rest for every week.
There is one day off every week. [i would say "I have one day off a week"]

This is my first job,But it reallly is a challenge for me.
This is my first job, and it really is a challenge for me. [it makes sense that you first job would be a challenge, so use "and"]

I entered into a new enverionment, it's different from school, many things are needed to learn,I feel so strange.
I entered into a new environment, it's different from school. There are many things i need to learn. I feel so strange. [at least in the US, we don't say "many" very much, we generally use "a lot of" or "lots of": There are a lot of/lots of things i need to learn.]

But I hope I could do it by my best.
But I hope I can do my best. [i think this sentence would make more sense as: "I feel so strange [previous sentence], but I will do my best"]

Good luck at your new job, don't let them take advantage of you just because you're new and this is your first job. They still need to respect you! 加油！

My First Job

Today is Sunday, and I don't need to work today. I have started working a new job about ten days ago as a Software Engineer, although, I've not graduated yet from my college.  There is one day for me to rest each week. This is my first job, and it reallly is a challenge for me.  I have entered into a new environment which is different from school.  There are many things needed to be learned, so I feel so strange. But I hope I can do my best.