Their both right. The first one is saying that you will go out with them if they have finished their job by the time of him going out. The second one is saying that yes you will go out with him if his job will be finished by a specific time. Which one you use depends on the exact situation your using it in.

Playing basketball with my son

Today is Sunday. The smog was gone today,and the sky was clear up. Due to the heavy air pollution in Beijing, We seldom do outdoor activities. We just stay at home with the windows closed, so the polluted air can't get indoors. On the other hand, we do need to be more physical active. Hence my family went to the small in park in my neighbourhood, where there is an small spare *do you mean a basketball court*. There I played basketball with my son. Actually he did not have any idea of how to play it, and he just picked up the ball from the ground. Anyway, he was so excited about it. I believe it is a good way to improve our relationship. I still remember my father seldom playing with me when i was little. I know lives were much tougher back then than those nowadays. People must struggled to raise a whole family. My parents my worked day and night to earn what we needed to satisfy basic needs. 

That is a pity, and I won't allow this to happen again during my son's childhood, and to leave some regret in his memories.
On the other hand, to keep healthy he needs to play in the sun everyday. How can we do that during such bad days in Beijing. Anyway, on most days, the official media is always suggesting that the public does not go outdoors or open windows due to the bad air condition.

Fast Food

In the past 30 years, the number of fast food restaurants have been increasing dramatically in Taiwan. Some laud its convenience and how it brings a new diet style to Taiwan. However, in this essay I intend to argue that fast food not just only affects the domestic economy directly but also poisons people’s health.

First of all, the popular fast food brand usually is from an international company, such as KFC or McDonalds. Once the international company decides to enter a specific country, the local restaurants providing the similar foods will be affected. Moreover, as it becomes more popular gradually, rice is not solely choice for people anymore, which means the domestic rice demand will drop down; as a result, the agriculture industry might be influenced, too. *You might want to think about rewriting the entire last sentence I don't exactly know what your trying to say*

Further and even More importantly, those foods such as fried chicken, hamburgers, and chips- which contain high fat and salt-might cause high blood pressure, obesity, and heart disease. It is also serious to remind you that those international fast food companies invest a lot money to make joyful advertisements on TV to attract children. For example, McDonalds emphasizes that they host birthday parties and provides a playground in the restaurant to cater to children’s interests. Having grown up eating fast food, people are likely to foster this diet habit through their adult lives.

By way of conclusion, I believe that fast food indeed brings convenient choice for eating to modern people, but we might lose something more valuable at the same time. We should pay more attention at how to foster local industries and cultivate the correct diet conception of in children.

A letter to a newspaper editor

I am writing you to tell you that there is be some a minor error in an article of your today's newspaper. I am a local people(in this sentence local implies that you a local person) of this city, and I have been living here for more than two decades since I was born. Hence I am very familiar with every corner of the city, and even can tell people the history of most famous buildings standing here.For instance, the LeiFeng tower, referred in one of your articles, is very near to my home. I frequently visit there with my friends and family since my childhood. The year when the tower was built was 1600, in the Ming Dynasty, not 1800, as your this essay says. Could you please fix this small error in the future, since it is one of the most important tourist attractions in our city and we should not confuse its history.

The girl I met online this morning

When I was working in my office, a girl from Brazil sent me a message from (from sounds ok, but if you replace it with via it sounds better) Skype. The message said that if I had trouble with my English I could contact her. I accepted her as my friend immediately, then we talked to each other on Skype (using it here just sounds weird). I got to know She told me that she had been studying English since she was three years old, so English was just like her native language. The time difference between us is 10 hours. It is relatively convenient for us to talk online. What I need urgently is to practice speaking English.
I will take IELTS next month, and I am weak at the speaking part. In fact, I have been studying it for more than two decades, but I have few chances to talk to native speakers in China. Hence my spoken skills are still not very good.
I plan to migrate to Australia this year, so this test is crucially important for me. It will determine whether or not I have a chance to move there.
The good news is she is on summer vacation now, so I suppose I have lots of time to speak with her to polish my English.
Although I have not seen her by now, I think she must be a pretty girl. The chats between us will be very helpful for my English communication skills.

Abstract of my project

As a new-style family service robot, a domestic cleaning robot must be able to accommodate itself to the complex indoor environment to complete clean-up tasks intelligently and efficiently. In order to gain intelligence it relies on its sensors and other external equipment, it is capable of going to the charging station automatically. At the same time the robot system requires functions for creating a map and path planning, for the sake of efficiency. On the basis of the tested (You can also use established) hardware, this paper researches the robot system software, which implements the functions of the robot automatically charging and creating maps. Firstly, this paper presents briefly the design of the robot's hardware and its components. The robot hardware includes three major components, namely the main body of the robot, recharging station and, the remote device. The robot has infrared receivers and collision sensors, the main function of it is cleaning. The charging station is the equipment which provides a place for the robot to recharge. The remote device can command the robot to create maps.
Secondly, the paper describes in detail the development process of the software system (Depending on what you mean you don't need system). To achieve high efficiency of the cleaning, regional maps must be established, to do this users use the remote device to control the movement of the robot. Through recording the movement of the robot, it can create a map. With a map, the robot can work in the region. In the process of cleaning, when detecting the voltage of its battery below a given value, it will begin to look for charging stations. The charging station emits an infrared signal, the robot knows the position of it because of this signal and thereby completes the docking.
Finally, the paper interprets the debugging course of the software system, and the
encountered problems and their solutions of them. Experimental results show that the
software system is robust, reliable and intelligent. This project has achieved the
expected goals of robot design.

Yes it is understandable, but you need to add a the between "of" and "jewelry sector.

a letter to a friend to offer some furniture to her

I will return to China next week, and I cherish the time we spend together and the help you provide for my study. I am writing you to tell you that I have a few pieces of furniture which you might be interested in. I listed the most important items to you.
A chair, which I bought last year, would be very suitable for you to place in front of your computer. The one you have now is so small that you probably feel a little uncomfortable if you sit in it for a long time. It would be good for your health and eyesight as well.
As you do not have a table, it is very inconvenient for you to have dinner with friends at home. You can take mine, and its size would be suitable for your living room.
Obviously, you cannot carry them with your bare hands in boxes. I suggest you hire a lorry to move them. Please call me and make sure if I'm available ahead of your arrival.

best regards,
Hitperson