question about time descriptions
There are some words can be used to describle a period of time. but i can not distinguish them about their correct usage.
(1) a while : sometimes we say "I just fall in thinking for a while?"
(2) a moment: At that moment, we had to roly on the meager income to keep our basicly life requirements. Is this grammatically?
(3) a period of time : In that period of time, I felt very sad because one of my best friend was died.

i doubt that above three sentences are made with complete correctness of grammar. so if not, tell me why and it's better to tell me how distinguish from them three?

Question

question about time descriptions
There are some words can be used to describle a period of time. but i can not distinguish them about their correct usage.
(1) a while : sometimes we say "I just fall in thinking for a while?"
(2) a moment: At that moment, we had to roly on the meager income to keep our basicly life requirements. Is this grammatically?
(3) a period of time : In that period of time, I felt very sad because one of my best friend was died.

i doubt that above three sentences are made with complete correctness of grammar. so if not, tell me why and it's better to tell me how distinguish from them three?

Answer

I think this would be the order of time usage:
"a moment" < "a while" < "a period of time"

Bob: 
Andy: "What happened Bob?"
Bob: "Oh I lost my focus because for a moment I thought I saw my High School crush."
a moment is like a time period from a few seconds to a few minutes.

Dan: 
George: "Let me help you up"
Dan: "Thanks, it's been a while since I've last skated"
a while can mean a long time.

David: "Why you look better than before John!  You used to look very pale and sick"
John: "Yea, there was a period of time when I didn't eat because I was sad that one of my best friend passed away."
一段时间

I don't know how to explain it very well off the top of my head.  But your third sentence is fairly correct. 1 and 2 didn't make sense...