Oh also " to do ( or carry out your job) more easier and quicker. Or to do your job (or carry out your job) more efficiently and easier. Efficiently= quicker / in a more timely fashion. Good luck!

The computer linking internet is a useful tool for my family to connect together, furthermore it may allow my family to go online shopping without walking to the physical shops on the streets in hot weather.

Yes. A little improvement. A computer and the INTERNET are the best TOOLS for xxxxx ( the computer itself is not media and you need internet for all the things you mention). THEY ( computer and internet) can be used to connect with familiy. THEY can also be used to find an on-line partner, and access on-line shopping. Personally, I feel a little reference to what's on the computer that is used also for what you are talking about, it's the internet and computer. The computer alone will not allow all of this, you do need the internet. But that's just my personal view and keep in mind I don't know the full nature of your essay! But just my view.