One of the possible models that at the moment seem to satisfy the queries you've posted:
(Team)-[:PLAYS]->(Match)
(Match)-[:HAS_REFEREE]->(Referee)
(Match)-[:PLAYED_IN]->(City)
The PLAYS relation could have a property to indicate if the team was the home team. You could also have a property on the PLAYS relation to indicate whether that team won or not. Or if winning is a big part of what you're looking for, you can create an extra relation such as (Team)-[:WON]->(Match) (though then you need to think about how to model draws. The absence of a WON relation on either of the two teams for a match could indicate a draw maybe).
1) All matches for a particular referee: Start at the referee, traverse through the Match to the Cities. You might index some unique property of the referee to be able to look him up quickly
2) All matches where the referee worked and the home team won: Start at the referee, find all his matches, filter on the WON relation/property and the home team property
3)All referees that have the highest count of wins for the home team: Same as above, start at all referees
4)Most active referees for a city: Start at the city, find all matches and their referees
You might move things around a bit depending on more questions that you want to answer (especially home team properties, WIN/LOSE relations or properties etc.)
And I don't think you need the root node at all. You can index all matches/cities/referees etc if you want to find all of them