Writeacher, here are some sentences I'd like you to revise. Thank you.

1) The teacher let the students off with a warning (let off the students is a mistake?)
2) I'm looking forward to my sister's letter. (I'm waiting impatiently for my sister's letter; I'm waiting with impatience for...I'm awaiting for you letter eagerly.. Are mistakes?)
3)The teapost came apart in my hands (broke in my hands is a mistake?) and I scalded myself.
4) The manager let him off the weekend because he had worked hard all the week.
5) Mary's father brought up two children by himself (on his own).
If a person works at a job, he or she is attracted by the financial aspect.
She is sick so Andrea has taken over the design of the machine.
If I were an employee, I would work at a career because the prospects of promotion and the development opportunities would motivate me most.

1) The teacher let the students off with a warning (let off the students is a mistake?) ...let the students off ... = correct. The direct object needs to be between the verb and its adverb (to make the phrasal verb).

2) I'm looking forward to my sister's letter. (I'm waiting impatiently for my sister's letter; I'm waiting with impatience for...I'm awaiting for your letter eagerly.. Are mistakes?)
None of these are mistakes, but the first phrasing is the very best, and the last one is very awkward.

3)The teapot came apart in my hands (broke in my hands is a mistake?) and I scalded myself.
Both ways of phrasing this are correct.

4) The manager let him off for the weekend because he had worked hard all week.

5) Mary's father brought up two children by himself (on his own).
Both ways to write this are fine.

If a person works at a job, he or she is attracted by the financial aspect.
OK

She is sick so Andrea has taken over the design of the machine.
OK

If I were an employee, I would work at a career because of the prospects of promotion and the development opportunities; those aspects would motivate me most.