Regarding the antenna, after looking at the datasheets in digikey, I think it is supposed to be a "normal mode helix".
To use this antenna, one end is connected to the antenna pin of your Tx or Rx module, and the other end is just soldered to a small pad on the circuit board, (for mechanical support, not connected electrically to anything).
I must question your use of the LTC5505 as a receiver.
This chip is intended to be used as an RF power monitor for a transmitter, it has very poor sensitivity for use as a reciever.
Your "short range" may be quite a bit shorter than you expect.
JimB