Can you check these sentences for me, please? Thank you.

1) Mary uses the internet mainly to carry out (also do/undertake) school research in History, Geography and Science.
2)Whenever she needs to get information, she looks it up on the net.
3) It's quick and easy since she just has to type a topic (I don't know how to call it) into the search bar (I can't remember the name for it) and in less than a second she gets all the information she needs.
4) If she couldn't use the net, it would take twice as long.
5) Samantha tried to use a translation programme on the net. She sent them the text and the programme translated it for her.
6) The translation wasn't very good and she didn't get good marks. Now once she gets the facts she needs, she puts them into her own words.
7) On the contrary, Mark downloads the information he needs from the net and uses it word for word (without changing anything).
8) Paul, on the other hand, (Can you suggest a better sentence connector) uses an online homework agency. He sends them his homework questions and they type him back the answers. He just has to hand them in (synonym) to his teachers.

1) Mary uses the Internet mainly to conduct school research in history, geography, and science.

2)Whenever she needs to get information, she looks it up on the 'net.

3) It's quick and easy since she just has to type her key words into the search engine, and in less than a second, she gets all the information she needs.

4) If she couldn't use the 'net, it would take much longer, perhaps even days.

5) Samantha tried to use a translation programme on the 'net. She entered the text, and the programme translated it for her.

6) The translation wasn't very good, however, and she didn't get good marks. Now once she gets the facts she needs, she puts them into her own words.

7) Another student, Mark, downloads the information he needs from the 'net and copies it word for word.

8) Finally, there's Paul, who uses an online homework agency. He sends them his homework questions, and they type him back the answers. He just has to submit them to his teachers.

Compare VERY carefully!

Internet (capital I)
'net (contraction for Internet)

Here are the corrections and improvements to the sentences you provided:

1) Mary uses the internet mainly for conducting school research in History, Geography, and Science.
2) Whenever she needs information, she searches for it online.
3) It's quick and easy for her; she just needs to enter a topic in the search bar and within a second, she gets all the information she needs.
4) Without the internet, it would take twice as long for her to gather the required information.
5) Samantha attempted to use an online translation program. She submitted the text, and the program translated it for her.
6) Unfortunately, the translation wasn't accurate, and she received low marks. Now, after she obtains the necessary facts, she rephrases them in her own words.
7) In contrast, Mark downloads information from the internet and uses it verbatim, without making any changes.
8) Conversely, Paul makes use of an online homework agency. He submits his homework questions to them, and they provide him with the answers. He just needs to hand in the completed work to his teachers.