I've seen some Chinese words like "YUEZHONG". Also in some other languages like Persian and Arabic I've seen words written with "zh". Are these two sounds pronounced in the same way? Is there any word in English using the same combination of letters? Is it right to use "zh" to imply the letter "j"?
Short answer: "zh" and "j" are not pronounced in the same way.
Using the International Phonetic Alphabet, the "zh" digraph would be transcribed as [ʒ], while the "j" letter would be [dʒ]. The "zh" sound occurs at the beginning of the name "Jacques" [ʒɔk], and in the middle of the word "leisure" [liʒɚ]. The "j" sound is two IPA symbols because it is a combination of two sounds, [d] (as in "dog") and [ʒ]; [dʒ] occurs at the beginning of the word "jock" [dʒɔk].
The "zh" and "j" sounds are definitely not identical to an English speaker. In fact, two words could be distinguished only by the difference between those two sounds. The following would represent such a minimal pair:
("Jock" and "Jacques", which I already mentioned, also only differ in that one sound.)
The reason you see many borrowed words using "zh" is because English lacks a standard letter to represent the [ʒ] sound. In French borrowings, it is "j", because "j" is always [ʒ] in French. Sometimes it is "si" (as in "lesion") because of a natural phonological process that occurs in English. So, there is no letter that always gets pronounced [ʒ]. But, in many languages that don't use Latin script, there is a distinct letter for [ʒ]. In these languages, "zh" is often the standard way to translate the sound [ʒ] from their orthographical system to the Latin one in an unambiguous way.
As to whether you can use "zh" to imply "j" — I am not certain what you mean by "imply", but since these are two different sounds, I think the answer is probably no.
Not always, but sometimes. This depends highly on the languages involved, and on how they’ve been transliterated into the Latin alphabet (if they’re not not normally written in it).
Zh almost(?) never occurs in English itself. In transliterations from Russian and other Cyrillic languages (eg Dr Zhivago, bozhe moi, …), it represents the sound [ʒ], a voiced version of the sound represented (in English) by sh [ʃ]. So, helpfully, the relationship of zh to sh here is just like the relationship of z to s. In transliterations from Chinese… well, let’s come back to that later.
The sound [ʒ] does occur in some English words, but it’s spelled differently: e.g. in beige, leisure.
J, on the other hand represents many, many different sounds. The main sound it represents in English, in for instance juice, is [dʒ], similar to zh [ʒ] but not quite the same. It’s (approximately) a voiced version of [tʃ], the ch sound in e.g. chop. It differs from [ʒ] in that at the beginning of the consonant, your tongue should touch the gums above the backs of your teeth, briefly but completely cutting off the airflow and then releasing it as the consonant starts.
In other Latin-alphabet languages, j represents various different sounds. In French, it does indeed mostly represent [ʒ]: e.g. jeune. In German, eg ja, it represents the sound given in English by consonantal y. In Spanish, it corresponds roughly to English h (depending on dialect and context).
In transliterations, j varies even more! In modern English-based transliterations of Russian (and other Cyrillic languages), j is usually not used, but in older and German-based transliterations, it’s often used like it is in German.
Finally, in modern transliterations of Chinese, zh and j represent two different phonemes which to English ears will typically both sound like the [dʒ] of juice; see John Purdy’s comments for details.
I'm not a linguistics major, but I can tell you that the two are not pronounced the same.
In layman's terms, zh is a voiced version of sh. The sh sound is normally made without engaging the vocal cords. If you add vocal sound to it, it will become zh.
In the j sound, you get ready to make the zh sound, but instead of leaving your tongue in that position, you push it up against the front of your palate, blocking the zh sound from coming out. Then you release it all at once and stop. This is important. The zh sound can be continuous, but the j sound stops almost instantly. If said alone, it will sound something like "juh".
zh does not represent any single Arabic letter but is very occasionally used to represent the 'ǧīm' as pronounced by Arabic speakers in former French colonies -Lebanon & Syria most especially. That's not altogether proper orthography -it's normally transliterated as 'j'- but the closest rendering of how certain Levantines and N.W. Africans with French as a second (or first) language employ it.
zhe [ﮊ] does exist in both Kurdish and Persian (and further east, too), and is pronounced the same way: in the luscious, mouth-filling style that Robusto so well describes above.