Is there an English word to describe a group of refrain words composed of two syllables e.g. pera-pera, meaning fluently, iki-iki meaning vividly?

The Japanese language has a special group of words which repeat mostly two syllable word like pera pera, para para, don don, suku suku, that are used adverbially for examples;

Pera pera eigowo hanasu– speak English fluently.

Iki Iki shiteiru – look vivid (fresh)

Don don iku – go fast

Para para furu – rain drizzlingly

Muka muka suru – feel sick (angry)

Pera pera mekuru – turn the page at random

Zuki zuki itamu – ache acutely

Suka suka tooru - pass smoothly

They look like onomatopoeias, but they are not. They don’t reflect any sound, and they are all used adverbially, not as interjections.

I don’t know whether such usage is special to Japanese language or not. Are there a lot of similar form of refrains of nonsensical (on their own) two - (sometimes one) syllable words in separation (unlike the type of crisscross, dillydally, riffraff which are single word) used exclusively adverbially except onomatopoeia (which is not my concern) in English and other languages. If there is, I'm curious to know how we call such a group of words or usages.

The general English term in linguistics for such repetitions is 'reduplication':

re·du·pli·ca·tion n.
....
3. Linguistics
a. A word formed by or containing a reduplicated element.
b. The added element in a word form that is reduplicated.

[reduplication. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved January 10 2016 from http://www.thefreedictionary.com/reduplication .]

In English, I was able to uncover approximately 75 exact (that is, the repetition is of the entire word, rather than of parts of the word) reduplicative verbs and nouns. Here are some examples:

• boo-boo, n.
• jaw-jaw, n. and v.
• ju-ju, n.
• la-la, v.
• no-no, n. and adj.
• tum-tum, n.
• yé-yé or yeah-yeah, adj. or n.
• yum-yum, n.

Exact reduplicative adverbs were fewer:

• flaunt-a-flaunt, adv. (also quasi-n.; obsolete; said to be onomatopoeic)
• chop-chop, adv. (and int.)
• now-now, adv.
• one-one, adv.
• piano piano, adv. (also as one word)
• pop-pop, adv.
• pretty-pretty, adv.
• so-so, adv. (and adj.)

Most of these exact reduplicative adverbs would not be well described as onomatopoeic.

'Reduplication' also describes phonetic duplication of parts of words, as in hubble-bubble.

With the exceptions of 'piano piano' and 'pretty-pretty', as far as I've been able to ascertain, the exact English examples are one-syllable words, like your Japanese example "don don".

This is called reduplication in English. You might be interested to read Key's 1965 paper on the topic. Here's another on Japanese.

As others have said, the repetitive structure of these words is described as reduplicative or the result of reduplication. In terms of function, these Japanese words are often called ideophones (see also the Wikipedia article); this refers to words that act a bit like onomatopoeia, but that represent ideas rather than sounds. English doesn't use ideophones much, if at all, but they are present in many other languages. They aren't always reduplicative as in Japanese, but they often are.