Are there some greetings or phrases particular to the Hui people?
Yes there are. Such language in Chinese is referred to as 回回话 Huíhui huà.

Thanks to user xiaohouzi79 for pointing out the book Muslim Chinese: Ethnic Nationalism in the People's Republic By Dru C. Gladney, which is partly viewable on Google Books.

This book contains a large appendix, A Select Glossary of Hui Chinese Islamic Terms on pages 393 to 421.

Here are some Hui greetings I found, which are transliterations from Arabic:


安色俩目阿莱空 Ān sè liǎ mù ā lái kōng - "Peace be to you"
安色俩目，尔莱库目 Ān sè liǎ mù, ěr lái kù mù - "Peace be with you"
色俩买提 Sè liǎ mǎi tí - "Peace be to you"


The glossary contains many terms relating directly to Islam and derived from Arabic, but there are many terms not pertaining to religion and terms from Persian, Turkic languages, and even wholly Chinese words used only by Hui or with additional Hui-specific senses.

Apparently Hui use Persian or Arabic numbers among themselves when bargaining so regular Chinese will not understand.

Here are a couple of other terms I found interesting:


番客 Fān kè - barbarian guest, foreigner
色瓦布 Sè wǎ bù - expression of thanks, "May Allah reward you"


As a traveller in China I'm interested to find out if Hui think of me as a 番客 and I will try saying 色瓦布 instead of 谢谢 next time I buy a meal from them.