This is a TVI only camera so will only work on a TVI system.
Does this dvr come with a hand held infra red remote control?
No, this unit does not come with an IR remote control.
Is this camera fixed-lens or varifocal? The web page describes it as "3.6mm Fixed Lens", but in the description tab I read "Lens: 2.8-12mm Varifocal".
This is a varifocal camera.
Price per pair or single?
TT-105a is sold as a pair, Price displayed will be for a pair.
How do you connect an IP camera to this DVR?
Firstly you will need to login to the unit , go to System -> Digital -> Channel type, then select the configuaration that supporst IP. An IP camera is then connected to this unit via it's RJ45 (lan port) using a network switch or POE switch.