A name like Tweety can be a problem when you start your career. It is a suitable nickname for friends, but it could cause some business people to take you less seriously than if you used a more common name because they will think of the silly cartoon character when they see your name. I think that your teacher is giving you good advice, and that a less cute name would make things easier. On the other hand, if you really identify with Tweety and wish to keep it, it's not something that will keep you from succeeding, it will just make it a little more difficult.
Have you thought about using an English phonetic spelling of your Chinese name? Many of the people I work with in the US don't have typical English names. They may have simplified the spelling of their name to make it easier for an English speaker to pronounce correctly, but there is no problem with them using something similar to their name in their native language.
Generally, when you read last name it really means family name or sur name.
But what do you mean when you say "family name"? Are your siblings also called ___ Adel Mahmoud Gad? Or just given-name some-other-name Gad?
If your whole family uses the names Adel Mahmoud Gad, you should use that as your "last name." I'm not sure about the rules in your culture, but many Spanish and Hispanic people have multiple family names, for example Gabriel García Márquez. His "last name" is not Márquez, it's García Márquez.
If you're working with a webform that's too stupid to accept spaces in a last name...I guess just use Gad.
As for middle names, fortunately, these are rarely required. If you decide that Gad is your family name, you could use both Adel and Mahmoud as your middle name. Again, if it's a webform, and inflexible, you'll just have to pick one. For official documents, it doesn't really matter what you use as a middle name, but just be consistent.
Best Answer
Quite a lot that is racist here. The 'Thomas Kalmaku' character in Green Lantern is an Eskimo/Inuk person originally from Alaska. The character was created in 1960, when Western attitudes towards racial and ethic stereotyping were often less progressive than today. Leading 'hero' figures in comics, films, etc, often had an ethnic-minority assistant or sidekick in a subordinate role (e.g. the Lone Ranger and Tonto)
Eskimo is an old fashioned term for the character's ethnic origin. Eskimo is a collective term used to refer to the Inuit (including the Alaskan Iñupiat, the Greenlandic Inuit, and the Inuit peoples of Canada) and the Yupik (or "Yuit") of eastern Siberia and Alaska.
People in many parts of the Arctic consider Eskimo a derogatory term because it was widely used by racist, non-native colonizers. In Canada's Central Arctic, Inuinnaq is the preferred, and in the eastern Canadian Arctic Inuit. In Alaska Inuk is used. The language is often called Inuktitut.
Grease monkey is a slang term for the occupation of mechanic (he is an aircraft mechanic). A mechanic's job has less status than that of a pilot (e.g. Green Lantern).
Thomas is his forename.
Pieface is his nickname (sometimes alleged to be a racist term from a stereotype of Inuks having round faces). When a person has a nickname it is often shown in brackets or quotes after the first name and before the surname e.g. Michael "Fathead" Harvey, Michael (Fathead) Harvey. In the comic text it is shown slanted.
Kalmaku is his surname (family name).