Writing sentences and paragraphs. Is this correct?

Paragraph 2
Dear Elizabeth,
I am anxious when I found out that you move back to town, and looking for job. My SBU manager, is currently hiring for a production manager. She is SBU manager for ACS. I think you should apply for the job. The requirements for the position are, working with offshore, meeting turnaround expectation, meeting quality expectation, answering phone calls, working one on one with the customer, working one on one with operators, setting up web meeting, testing new programs, ordering supplies, making decisions on hours that are needed work daily, and approving time scheduling off with the co-workers. You are always willing to learn any new opportunities that are offer up, compassionate about other feeling, and extremely good at multi-tasking. It would be a good access to have you join our team.
All my best,
Levon Couch

Suggestions given in caps. You need to be more aware of matching tenses and persons, along with your use of commas.

Dear Elizabeth, (COLON)

I am (PAST TENSE) anxious (COMMA) when I found out that you move(D) back to town, (NO COMMA) and (WERE) looking for job. My SBU (SPELL OUT FIRST TIME) manager, (NO COMMA) is currently hiring for a production manager. She is SBU manager for ACS (SPELL OUT FIRST TIME). I think you should apply for the job.

USE NEW PARAGRAPH TO INDICATE CHANGE IN TOPIC, PLACE, PERSON OR TIME.

The requirements for the position are, working with offshore (WHAT?), meeting turnaround expectation(S), meeting quality expectation(S), answering phone calls, working one on one with the customer(S), working one on one with operators, setting up web meeting(S), testing new programs, ordering supplies, making decisions on hours that are needed work daily, and approving time scheduling off (DELETE "OFF") with the co-workers. You always ("NEED TO BE") willing to learn any new opportunities that are offer ("COME") up, ("BE") compassionate about other(S') feeling(S), and extremely good at multi-tasking. It would be a good access (RIGHT TERM?) to have you join our team.

All my best,
Levon Couch

http://grammar.ccc.commnet.edu/grammar/commas.htm

In the future, if nobody is available to proofread your work, you can do this yourself. After writing your material, put it aside for a day — at least several hours. (This breaks mental sets you might have that keep you from noticing problems.) Then read it aloud as if you were reading someone else's work. (Reading aloud slows down your reading, so you are less likely to skip over problems.)

If your reading goes smoothly, that is fine. However, wherever you "stumble" in your reading, other persons are likely to have a problem in reading your material. Those "stumbles" indicate areas that need revising.

Another option, if it is available on your computer, is to have the computer read it to you.

Also, make use of "Spelling and Grammar" under "Tools" in your word processing program.

Once you have made your revisions, repeat the process above. Good papers often require many drafts.

Paragraph 2: Writing Sentences and Paragraphs - Explanation and Revision

In the given paragraph, there are a few areas where sentence structure and clarity can be improved. Let's break it down and revise accordingly:

Original Paragraph:
Dear Elizabeth,
I am anxious when I found out that you move back to town, and looking for a job. My SBU manager is currently hiring for a production manager. She is an SBU manager for ACS. I think you should apply for the job. The requirements for the position are working with offshore, meeting turnaround expectations, meeting quality expectations, answering phone calls, working one-on-one with the customer, working one-on-one with operators, setting up web meetings, testing new programs, ordering supplies, making decisions on hours that are needed to work daily, and approving time scheduling off with co-workers. You are always willing to learn any new opportunities that are offered up, compassionate about other's feelings, and extremely good at multitasking. It would be a good addition to have you join our team.
All my best,
Levon Couch

Revised Paragraph:
Dear Elizabeth,

I was thrilled to hear that you have moved back to town and are in search of a job. Currently, my SBU manager at ACS is hiring for a production manager position. Considering your skills and qualifications, I strongly believe you should apply for this job opportunity. The requirements for the position include working with offshore teams, meeting turnaround and quality expectations, answering phone calls, collaborating one-on-one with customers and operators, arranging web meetings, testing new programs, ordering supplies, making daily work-hour decisions, and coordinating time-off schedules with co-workers.

I have always admired your willingness to embrace new opportunities, your compassion towards others, and your exceptional multitasking abilities. Your addition to our team would be greatly valued.

All my best,
Levon Couch

In the revised version, the content remains the same, but the sentences are structured more clearly and concisely. The revised paragraph maintains a professional tone and effectively conveys the intention.