They are jade (玉), not emerald. Emerald (绿宝石) is not jade. There are two types of real jade (Jadeite 翡翠 - usually from Burma 缅甸, and Nephrite 玉 - Usually from China).
Photos 1, 2, 3, and 5 are genuine Grade A (natural color) jade (Burmese Jadeite 缅甸翡翠).
Photo 4 is Chinese Xiu jade (岫玉).
Most of Burmese jadeite (翡翠) items for sale come with certificates of authenticity issued by approved gem labs in Hong Kong or Mainland China.
The higher end ones like Photos 3 and 5 were carved by my family member's business in Hong Kong. They have been in jade business for more than thirty years in Hong Kong, and they import raw jadeite stones from Burma and carve them into high quality jade jewelry and statues.
国际上, 被认可的真玉是指翡翠(jadeite)和软玉(nephrite)
中国人通常叫所有绿色石头做玉, 但我们跟随国际标准.
我们出售的产品大约百分之九十是纯天然颜色(A货)翡翠(grade A jadeite).
其他有小量软玉(grade A nephrite)和中国岫玉(Grade A chinese xiu jade).也有很少数上色翡翠(产品上有清楚说明是grade B/C)