What is the difference between “ɪ”, "i", “i:”? Are these two same “ɪ”, "i" and won't be wrong if interchanged while transcripting? For example: Is it correct to write either /ʃɪp/ or /ʃip/ in case of IPA transciption of the word "Ship"?
<i> has been used to represent both the vowels in ship and sheep. You can never tell what sound an IPA symbol represents just by looking at it by itself, because there are competing conventions. You have to look at what words it's used to represent or what other symbols are used in the same system. As the Handbook of the International Phonetic Association (1999: 30) puts it:
[T]he contrast between the words bead and bid has phonetic correlates in both vowel quality and vowel duration. A phonemic representation which explicitly notes this might use the symbols /iː/ and /ɪ/ ... But it is equally possible unambiguously to represent these phonemes as /iː/ and /i/ ..., or as /i/ and /ɪ/ ... All three pairs of symbols are in accord with the principles of the IPA ... The IPA does not provide a phonological analysis for a particular language, let alone a single 'correct' transcription, but rather the resources to express any analysis so that it is widely understood.
The three types of notation (/iː/–/ɪ/, /iː/–/i/, and /i/–/ɪ/) are known as "qualitative-quantitative", "quantitative", and "qualitative", respectively. The quantitative and qualitative transcriptions coexisted for a long time, but the latter is usually favored in North America because the contrast in duration is not as robust there as in England. In the UK, the quantitative type used to be popular, but has largely been replaced by the qualitative-quantitative since around 1970.
The quantitative notation was used in highly influential publications such as Daniel Jones's English Pronouncing Dictionary (1917)—hence also known as the "Jonesian" notation—and the first editions of the Oxford Advanced Learner's Dictionary (1948), so you might still encounter it especially in educational material such as bilingual dictionaries, even though recent publications coming directly out of the UK overwhelmingly use the qualitative-quantitative, or "Gimsonian", notation, which was formalized by A.C. Gimson, who succeeded Jones.
Few if any American dictionaries aimed at native speakers use IPA, but learner's dictionaries from the US tend to opt for the qualitative system.
An additional complication unique to this trio of symbols is that some qualitative-quantitative conventions employ all three of them. In such a system, <i> refers to a situation, typically exemplified by happy, where it used to be pronounced by a majority like /ɪ/ until some time in the 20th century but now it's most often pronounced like /iː/. This does not mean that there is a separate sound; it just means "/iː/ or /ɪ/", and for most modern learners it can be equated with /iː/. See this Wikipedia section for more.
"i", “i:” have the same quality in IPA symbols; this means that on the diagrams of pronunciation (back-front vs open-close) they are found at the same place (front (front of the mouth), close (mouth closed) ; the only difference is the length. “ɪ” is pronounced with the mouth less closed and not so near to the front.
No, it is not correct to write either /ʃɪp/ or /ʃip/ in case of IPA transcription of the word "Ship". The only pronunciation is /ʃɪp/.
You might find "i" in "sheep" instead of "i:", this being so because of so called pre-fortis clipping (/p,t,k,f,θ,s,ʃ,tʃ/ the fortis consonants make the vowel shorter).