1. Time gap between tow surveys or longitudinal study is not fixed . It totally depend upon the nature and objectives of the study. So it can not be decided by some else.

2. SEM can be used only if you are able to identify/ define ( through EFA and CFA) a model in literature.

3. to compare before and after results . you can use before and after experimental study design to compare or dependent t test.

There is no set single number. In my experience 1 month is probably the minimum. When following subjects over an extended time especially with less educated six months works better than one year which result in an additional 20-30%  attrition.

There is 

if anyone has any references related to the minimum period , please share.. 

Bekele Belayihun,

You should go for student's paired t test instead of SEM,

In paired t test, if you find your data is skewed and violates the assumption of normality in distribution, then you go for its substituting test of "the Wilcoxon Signed-Rank test".

For longitudinal study, at least 6 months of time for data collection is desired, but one should search for minimum time scale required to conduct it.

Thanks

Agreed. Time gap between 2 surveys is not fixed or a set formula. It does indeed depend upon the research objectives of the study. Typically, 2-3 months can suffice in social science studies but have seen longer gaps as well.