1. The wraith's gun is so weak.
(i.e., The ghost's gun. OK; Possessor: It tells us whose gun.)
2. The wraith gun is so weak.
(i.e., The ghost gun. OK; Adjective: It tells us what kind of gun.)
3. Jack's gun is so weak.
(OK; Possessor: It tells us whose gun. Please note, 'weak' is the wrong adjective. That is, guns are not described as 'weak'.
4. Jack gun is so weak. (For people, you have to use 'apostrophe s' right?)
(Not OK. As you've said, "you have to use 'aspostrophe -s')
If, on the other hand, "Jack/jack" refers to a type of gun, then it would function as an adjective, but you'd need to add a determiner/article, like this,
EX: A Jack/jack gun...
EX: The Jack/jack gun...
5. I have a Sony TV.
(OK; Adjective)
6. I have Jack's TV.
(OK; Possessor)
7. I have Sony's TV.
(OK: Possessor. Note that, Sony, a brand name, is also the name of a company (i.e., The TV belongs to Sony Corporation/to Jack/to Mary).
8. Jack's Catch-phase: Practice makes perfect.
(OK; Jack's words. That is, the words 'Practice makes perfect' form a catch-phrase; that catch-phrase belongs to Jack.)
9. Viewsonic (Viewsonic is a monitor brand) Catch-phase: See the difference.
If Viewsonic is the name of a company, then "Viewsonic's catch-phrase" would be correct; If viewsonic is type of brand, the as an adjective it describes what kind of catch-phrase: it's a viewsonic catch-phrase.
10. Jack catch-phase: Practice makes perfect. (Is this incorrect? b/c for people you have to use 'Jack's'?)
Jack's catch-phrase. (OK)
Jack catch-phrase. (Not OK if you want it to mean, possessor, but OK if you want it to mean, an idiotic/worthless catch-phrase). That is, 'jack' has more than one meaning.
10. Viewsonic's Catch-phase: See the difference.
(OK; Possessor. "Viewsonic" is a proper noun; it's the name of a brand or company.)
All the best,
(i.e., The ghost's gun. OK; Possessor: It tells us whose gun.)
2. The wraith gun is so weak.
(i.e., The ghost gun. OK; Adjective: It tells us what kind of gun.)
3. Jack's gun is so weak.
(OK; Possessor: It tells us whose gun. Please note, 'weak' is the wrong adjective. That is, guns are not described as 'weak'.
4. Jack gun is so weak. (For people, you have to use 'apostrophe s' right?)
(Not OK. As you've said, "you have to use 'aspostrophe -s')
EX: A Jack/jack gun...
EX: The Jack/jack gun...
5. I have a Sony TV.
(OK; Adjective)
6. I have Jack's TV.
(OK; Possessor)
7. I have Sony's TV.
(OK: Possessor. Note that, Sony, a brand name, is also the name of a company (i.e., The TV belongs to Sony Corporation/to Jack/to Mary).
8. Jack's Catch-phase: Practice makes perfect.
(OK; Jack's words. That is, the words 'Practice makes perfect' form a catch-phrase; that catch-phrase belongs to Jack.)
9. Viewsonic (Viewsonic is a monitor brand) Catch-phase: See the difference.
If Viewsonic is the name of a company, then "Viewsonic's catch-phrase" would be correct; If viewsonic is type of brand, the as an adjective it describes what kind of catch-phrase: it's a viewsonic catch-phrase.
10. Jack catch-phase: Practice makes perfect. (Is this incorrect? b/c for people you have to use 'Jack's'?)
Jack's catch-phrase. (OK)
Jack catch-phrase. (Not OK if you want it to mean, possessor, but OK if you want it to mean, an idiotic/worthless catch-phrase). That is, 'jack' has more than one meaning.
10. Viewsonic's Catch-phase: See the difference.
(OK; Possessor. "Viewsonic" is a proper noun; it's the name of a brand or company.)
All the best,