I have open orders of currency pairs A, B, and C. Is there a way to get the expert to recognize that there is no open order of currency pair D?

There are a few ways to do it. The easiest might be to use the code in the moving average sample from MQ that came with MT4. What it does is calculate current orders in this function:

//+------------------------------------------------------------------+
//| Calculate open positions                                         |
//+------------------------------------------------------------------+
int CalculateCurrentOrders(string symbol)
  {
   int buys=0,sells=0;
//----
   for(int i=0;i<OrdersTotal();i++)
     {
      if(OrderSelect(i,SELECT_BY_POS,MODE_TRADES)==false) break;
      if(OrderSymbol()==Symbol() && OrderMagicNumber()==MAGICMA)
        {
         if(OrderType()==OP_BUY)  buys++;
         if(OrderType()==OP_SELL) sells++;
        }
     }
//---- return orders volume
   if(buys>0) return(buys);
   else       return(-sells);
  }

And then in the start function, it only will seek to open an order if it doesn't already have one open:

   if(CalculateCurrentOrders(Symbol())==0) CheckForOpen();
   else                                    CheckForClose();

Those are at least good pieces to start with. You could adjust it so instead of counting orders, you could just return true/false if there are any orders, and then make that function call a condition of the EA's open order test. Pretty similar to this one, very slightly different.

void GbpUsdBuy() {
  bool
    result,
    GbpUsdopen;
  double
    GbpUsdBid=MarketInfo("GBPUSD",MODE_BID),
    GbpUsdAsk=MarketInfo("GBPUSD",MODE_ASK),
    GbpUsdPoint=MarketInfo("GBPUSD",MODE_POINT);
 for(int GbpUsd=0;GbpUsd<OrdersTotal();GbpUsd++) {
  if(OrderSelect(GbpUsd,SELECT_BY_POS,MODE_TRADES)==false) break;
  if(OrderMagicNumber()!=Number || OrderSymbol()!="GBPUSD") continue;
  if(OrderType()==OP_BUY) GbpUsdopen=1;}
  if(GbpUsdopen==0)
  {result=OrderSend("GBPUSD",OP_BUY,lot(),GbpUsdAsk,3,GbpUsdBid-GbpUsdPoint*SL,GbpUsdBid+GbpUsdPoint*TP,"",Number,0,OrangeRed);
  if(result!=TRUE) Print("LastError = ",GetLastError());return;if(result==135) RefreshRates();}}

void GbpUsdSell() {
  bool
    result,
    GbpUsdopen;
  double
    GbpUsdBid=MarketInfo("GBPUSD",MODE_BID),
    GbpUsdAsk=MarketInfo("GBPUSD",MODE_ASK),
    GbpUsdPoint=MarketInfo("GBPUSD",MODE_POINT);
 for(int GbpUsd=0;GbpUsd<OrdersTotal();GbpUsd++) {
  if(OrderSelect(GbpUsd,SELECT_BY_POS,MODE_TRADES)==false) break;
  if(OrderMagicNumber()!=Number || OrderSymbol()!="GBPUSD") continue;
  if(OrderType()==OP_SELL) GbpUsdopen=1;}
  if(GbpUsdopen==0)
  {result=OrderSend("GBPUSD",OP_SELL,lot(),GbpUsdBid,3,GbpUsdAsk+GbpUsdPoint*SL,GbpUsdAsk-GbpUsdPoint*TP,"",Number,0,OrangeRed);
  if(result!=TRUE) Print("LastError = ",GetLastError());return;if(result==135) RefreshRates();}}


void EurUsdBuy() {
  bool
    result,
    EurUsdopen;
  double
    EurUsdBid=MarketInfo("EURUSD",MODE_BID),
    EurUsdAsk=MarketInfo("EURUSD",MODE_ASK),
    EurUsdPoint=MarketInfo("EURUSD",MODE_POINT);
 for(int EurUsd=0;EurUsd<OrdersTotal();EurUsd++) {
  if(OrderSelect(EurUsd,SELECT_BY_POS,MODE_TRADES)==false) break;
  if(OrderMagicNumber()!=Number || OrderSymbol()!="EURUSD") continue;
  if(OrderType()==OP_BUY) EurUsdopen=1;}
  if(EurUsdopen==0)
  {result=OrderSend("EURUSD",OP_BUY,lot(),EurUsdAsk,3,EurUsdBid-EurUsdPoint*SL,EurUsdBid+EurUsdPoint*TP,"",Number,0,OrangeRed);
  if(result!=TRUE) Print("LastError = ",GetLastError());return;if(result==135) RefreshRates();}}

void EurUsdSell() {
 bool
   result,
   EurUsdopen;
 double
   EurUsdBid=MarketInfo("EURUSD",MODE_BID),
   EurUsdAsk=MarketInfo("EURUSD",MODE_ASK),
   EurUsdPoint=MarketInfo("EURUSD",MODE_POINT);
 for(int EurUsd=0;EurUsd<OrdersTotal();EurUsd++) {
  if(OrderSelect(EurUsd,SELECT_BY_POS,MODE_TRADES)==false) break;
  if(OrderMagicNumber()!=Number || OrderSymbol()!="EURUSD") continue;
  if(OrderType()==OP_SELL) EurUsdopen=1;}
  if(EurUsdopen==0)
  {result=OrderSend("EURUSD",OP_SELL,lot(),EurUsdBid,3,EurUsdAsk+EurUsdPoint*SL,EurUsdAsk-EurUsdPoint*TP,"",Number,0,OrangeRed);
  if(result!=TRUE) Print("LastError = ",GetLastError());return;if(result==135) RefreshRates();}}

 for(i=0;i<total;i++)
      {
      OrderSelect(i, SELECT_BY_POS, MODE_TRADES);
         {
         if(OrderSymbol()==Symbol())
            {
            sym++;
            }
         if(OrderSymbol()!=Symbol())
            {
            tok++;
            }
         }
      }