The Acoms, Futaba and Hitec TXs that I have have all had a moulded-in tray for AA cells - a pre-made pack just wouldn't fit.
At the prices Howes quotes I would be amazed if crystals were included, so they will be an "extra".
The original outfit from ebay may have had a battery harness (battery holder, switch, plug and wiring) for the RX.
If the servo is vaguely modern, with three wires, it will be compatible with any modern RX, even it it needs a few bits of the plug moulding sanding back as all manufacturers want to lock you in to their brand. As long as the wires go "black, red, white" and the black, when plugged in, is nearest the outside edge of the RX case, no problems. Sometimes brown is used instead of black, and yellow instead of white.
If your ESC has a label saying "BEC" you probably wont need a RX battery, it will derive the RX and servo supply from the main battery.