New lens

I think it would help if you gave us an idea of what subjects interest you.

Originally Posted by Karn

I'm going to buy a new lens or two, I like to shoot indoors in low lighting, occasionally outdoors in sunlight, I really dislike flash, I love blurred backgrounds, the blurrier the better, I somewhat understand d.o.f but every lens is different, here are some FX lenses I'm looking at for my d7200

AF-S NIKKOR 200-500mm f/5.6E ED VR (why does this work with the 1.4x but not 1.7x or 2x converter?) 1400$

When you add a teleconverter, you lose stops of light. A 1.4x teleconverter on the Nikon 200-500 would make the largest aperture an f/8 or f/9. a 2x teleconverter on that lens would make it f/11. Most likely your camera would struggle to achieve focus in such low light.

I am not familiar with the lenses you mentioned so won't comment other than to say the faster the lens, the better it will AF in low light. If you shoot a lot in low light, faster lenses work much better.

If you shoot indoors you should really get to know how to use a flash and not the popup one built into your camera.

For indoors I don't see a use for the 200-500/5.6 unless your definition of indoors is a sports arena. For kids the 35/1.4 is going to be the best out of what you listed and any of the 50's will work for just about everything. Not mentioned but worth a look is the 85/1.8 for reach and portraits. If it can only be one lens then I'd option for one of the 50's.

This is a hard one to answer as you have basically described 2 different shooting scenarios

The 200-500 is an amazing piece of kit and great for fast moving things outside, be that kids or wildlife so I would say yes get that.

On the other side it depends on the size of room you have, remember that the 7200 is a crop so you will be getting a longer focal length. That being said when I had my D500 my favourite lens by the end of it was the 50mm 1.4 and they can be picked up very cheap second hand.