Trouble with solid state relay
It's a Solid State Relay - put an actual load (the light, or some other light, etc.) on it to test function - a voltmeter drawing no current may well give misleading readings (with a load present the voltmeter should give an accurate reading.)

For the sake of testing, use a 9V battery if the operation of the sensor is questionable. With battery connected, the load should be on, with battery disconnected, load should be off.

For the sensor, you will either need to drill a hole or mount it differently so that it can work, or change to a different type of sensor. If the sensor is "aways on" and it's connected, then the relay will be always on as well, so that may be the other answer to question #1.

Edit - regarding sensor.

You need to PROVIDE some Voltage for the (sensor's) relay to switch. The Sensor output is a "dry relay contact" - it's a switch, that's all. The sensor does not apply any power to it.

The SSR's input is looking for 3-32V dc.

You need to connect some source of 3-32V DC to the sensor so that when the sensor closes its output, the voltage is applied to the SSR's input. The 48V is a maximum rating on the sensor's switch, but the 32V rating on the SSRs input rules this one.

IF and ONLY IF you are feeding the sensor DC (it appears to take AC or DC) you could connect from the - power for the sensor to the #4 - terminal of the SSR, and connect from the + power for the sensor to one yellow wire on the sensor, and connect the other yellow wire on the sensor to the #3 + terminal on the SSR. Though I have to say at this point this is also verging into "you appear to be wiring things up that you don't quite understand, and you can get hurt doing that" territory. The SSR input is DC only - if you are feeding the sensor AC, you need a different source of DC, connected the same way (- to -, + to relay, relay to +)