Inside the caves the temperature is a fairly constant 8 - 12º Celsius, so bring a warm sweater/fleece jacket. 
 

Yes, however please note at the entrance to the caves there is a large rock overhang and bending is required to pass this section.  

There are also steps and often the walkways are wet, so care is required in the subdued light.

Te Anau is about a 2 hour 30 minute drive from Queenstown and around 5 hours from Dunedin.

From Manapouri, it's around a 30 minute drive.