Analysis of gai2

The first step in analysing the use of gai2 is to compare its use with Mandarin so we can deduce some guidelines about its use

gai2 mih4gai5  個乜個 - [What is this?] In Mandarin, we would say: shi4 shen2me5 是什麼

gai2 ua2 gai5 個我個 - [This is mine] In Mandarin, we would say: shi4 wo3 de5 是我的

So from these two examples, we can say one aspect of gai2 is that it has the same meaning as the Mandarin shi4 是

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Second use of gai2

gai2nang5 haoⁿ3 cia1 個人好車 - [he likes to boast] Mandarin = zhe4 ren2 xi3huan5 kua1kou3  這人喜歡誇口

個人 = 這人 = this person

So the second use of gai2 is that it has the same meaning as the Mandarin word zhe4 這: this 

The third use of gai2: gai2 here has the same meaning as dao4di3 到底 : 

Gai2 si5 zo3ni5? 個咋呢 - [What is the matter?] Mandarin = dao4di3 zen3me5le5 到底怎麼了

gai2 also has the same meaning as jiu1jing4 究竟 which has a similar meaning to dao4di3 到底 : for example see below:

gai2 u6 iaⁿ2 a7 bho5 個有影啊無 [Is it true or not?] In Mandarin it would be said as: jiu1jing4 you3 mei2you3 zhe4  hui2shi4 究竟有沒有這回事

Fourth use of gai2: gai2 here has the same meaning as ba3 把 in Mandarin 

gai2 i1 liah8 lai5 個伊掠來 - [bring it here] Mandarin would be ba3 ta1 na2lai2 把它拿來

gai2 i1 ziah8 loh8ke3 個伊食落去 - [take and consume it] Mandarin: ba3 ta1 chi1 xia4qu4 把它吃下去

so gai2 in Mandarin can mean

1. 是
2. 這
3. 到底 or 究竟
4. 把