What are the prerequisites before running Holt Winters Model?
1) Holt-Winters doesn't require stationarity the way an ARIMA model does, so you don't need to perform any of the steps you mention. However Holt-Winters is specifically designed for seasonal data, so don't bother applying it unless you have good reason to think your data is seasonal. 

2) In the basic formulation of Holt-Winters, no, it can't. More recent implementations of Holt-Winters use the state space approach to time series modeling, and it might be possible to do so using the state space approach - although even that is still in debate. BSTS is another state space model with a structure similar to Holt-Winters, and that approach does allow for causal factors. You should check that. 

3) No, you don't need to. The whole point of Holt-Winters is that it accounts for seasonality, so you don't need to adjust for it. 

4) See here. Holt-Winters can't handle missing values, but other methods can. You should be careful with Outliers, since you don't know whether an outlier is a "real" outlier, a seasonal spike, or a causally driven event. For example in a sales time series, your spike might be a true outlier, or it might be an event like Black Friday, or it might be the result of a promotion and advertising campaign.