Hi!
I was able to get all the orders, but I do not understand how to get all the positions (I have two exactly).
To get orders I use code like the next:

IEngine engine = context.getEngine();
...
List<IOrder> orders = engine.getOrders();

I try to get positions getting history orders (code looks like that one):

IHistory history = context.getHistory();
...
List<IOrder> orders = history.getOrdersHistory(Instrument.EURUSD, timeFrom.getTimeInMillis(), timeTo.getTimeInMillis());

But I get nothing. Is my approach correct and mistake only in instrument or time, or there is another method to get positions?

In fact IOrder represents a position - a main order with optionally attached stop loss and take profit orders.
You can retrieve like this only the orders of IOrder.State.CLOSED, see:
https://www.dukascopy.com/wiki/#Order_history