1) Do we include all the variables during multiple imputation regardless of their missing value status or include only the ones which have missing values for multiple imputation
2) is it good to do a univariate analysis in the binary logisitic regression by running regression one variable at a time and then picking variables that are less than 0.2 in p value and then run them in the multivariate form of binary logistic regression?
Since you usually assume missing at random (MAR) conditional on the observed data when doing multiple imputation, it is important to include all the data that may give information on the unobserved missing value or the reason for why it is missing in the multiple imputation. If key variables are ommitted, then the assumptions behind the imputations are likely to be violated.
Deciding on the variables that should be included based on some logistic regression for the missingness indicator (presumably that was the idea of what was mentioned?) is almost certainly not a good idea for a number of reasons: Firstly, this would say nothing about how much information on the missing values a variable contains. Secondly, if there are few missing values, no or hardly any variables would be associated with a low p-values despite possibly being extremely important. Thirdly, almost always when you look at strategies that involve doing some kind of hypothesis tests to decide how to conduct an analysis, these strategies tend to have poor properties (I'm generalizing, but I'd be interested to hear of any case where such an approach has been shown to have good properties).
On point 1, if I understand the question, if you include variables that have no missing values, they will not be changed, but using them as predictors may well be useful.
