Learn English – what is the difference “I am prepared for something” and “I prepared for something”

In many contexts, the meanings are pretty much the same, but you might hear finished more often than completed in casual conversation. For example:

I've finished my shopping.
She finished the song.
He finished the race.

I could use completed in those sentences – the meaning wouldn't change, but the register might sound off.

The word completed can convey some sense of accomplishment. In the context of a race, it might work when the race is a major achievement:

He completed his first marathon last year.

Homework, though, is not really a major achievement, so I think you'd hear finished more often in casual conversation:

“Joey, where are you going? Did you finish your homework?”

That said, you might see completed in more formal contexts, such as a paper on education, or a course syllabus:

Students must complete six homework assignments during the semester.

As the others have said:

I might work more this week.

Implies that you have some sort of control over the situation, whereas

I might be working more this week.

Implies that you don't really have the choice.

can't i say : "There is traffic on the highway so i might arrive late."

Yes you can. And the reason this shows that you don't have control is because of the mention of the traffic.

Also context can play a big difference, if somebody invited me to a party in a week's time and I said

I'll be there, but I might be late.

That would imply that I have control, because I knew about it a week in advance, whereas if I sent that message on the day, it would imply that I have no control.

I hope this helped.

As for your second set of questions, both make sense. However I would have said "I have to work more today" to show that I have to do it, not that I really want to do it.