Yeah, both "xem" and "thử xem" in these sentences mean suggestion
"Chị nghĩ xem việc đó có nên làm không?" means "Do you think whether I should do that or not"
"Cam ngon lắm, anh ăn thử xem" means "This orange tastes good, you should try!"
"Anh thử hỏi ông ấy xem" means "You should/can try asking him"
"Anh tìm xem ông ấy ở đâu" means "You should find where he is" (if this is advice) or "Find him!" (if this is an order)
As you see, those sentences above mean suggestion and "thử xem" and "xem" mean "try" or "think" (depends on situations). For example:
"Chị xem anh ta có dại dột không?" mean "Do you think he was too crazy?"
or
"Bạn xem thử cái áo này có đẹp không" means "Do you see/think if this shirt is nice?"