Note Air NZ operates from Terminal 3 at Heathrow, not Terminal 2.

That connection is too tight. It's a long way (65 miles by road) from Stansted to Heathrow. Easiest way is the non-stop bus between the two. It goes every hour, leaving Stansted at 05 minutes past each hour, and is scheduled to take 1 hour 20 minutes. You are unlikely to get to Heathrow quicker by making two changes of train across Central London. Bus operator is Jetlink, full details on www.gobycoach.com

For hotel at Stansted try Hilton National Stansted, who do transfers to/from the terminal. They are on the web.

Ryanair (who are Southwest without the peanuts) schedule their aircraft to have 20-30 minute turnarounds all day, so the old "late planes get later" adage applies. However, for many the reduced fares make it worthwhile. Baggage delivery at Stansted is about a mile away from where the aircraft park - enough said!