DAX, measure, date on report between start and end dates

[purpur]

Hello all

I am relatively new with DAX. I have tried to pick my brains for quite some time now with DAX measure; rather unsuccesfully though.

Data in question is HR data. Each employment contract has start date and end date as shown in picture below.

 

Both dates have a relationship to calendar table, also shown below (just a part of the actual model which has several more tables).

I would like to know how I can write a measure

1. which gives me number of employees at chosen date
2. which gives me number of employees during chosen month or year (even a day within chosen time period should mean the person is counted in the results

I have tried creating a measure for personnel amount at chosen date with and without calendar relationships. I have tried using DAX formula

CALCULATE(COUNT('Contract'[DimTyontekija_Id]);filter('Contract';'Contract'[Start Date] <= max('Calendar'[Date]) || 'Contract'[End Date] >= min('Calendar'[Date])))

but changing the date gives blank result. I suppose inactive relationships are the cause for this, but as far as I understand I can't use USERELATIONSHIP in filter. Or the culprit might be entirely something else. 

What comes to the second measure I would like to create - I have not even started banging my head at my table yet.

Any and all help would be greatly appreciated.

- mira