When we apply a model to let's say 100 time series using StatsForecast, does it come up with one fit for all of them or 100 different fits? So for example in case of ARIMA, is it trying to find the best p,d,q that is optimal overall for all the series or does it fit to individual series and calculate 100 p,d,q pairs?

All models of stataforecast are local, therefore in your case you would have 100 diferented models for hundred different individual time series.