NAV NDB OTS

It is the policy of the faa to decommission them as this inevitably happens to the rest of them. They are too expensive to fix. I guess enjoy them for the next few years?

Certain ones will not be repaired as they go out of service due to a variety of reasons. Some will be hanging around for awhile still. Eventually they will be phased out all together.

As for an airport with ONLY an NDB approach; sometimes it is allowed to use GPS 'in lieu of' certain navigational facilities. Here is an example where the LOM is OTS but a GPS waypoint could be used 'in lieu of':

So NDB's are going away slowly?

Here are a few articles on the process:

FAA Explains Instrument Approach Procedure Shutdowns | Aviation International News
So long to 216 NDB approach procedures - AOPA

As you can see from the dates on the articles, this has been an ongoing process over years and will continue so.

So it may not be on future instrument rating exams then.

Probably because the ADF offers a lot of fertile ground for exam questions. They should have all been shut down years ago. I bet if you took up a collection from airline pilots to shut down the ADF/NDB approaches at rural airports you would probably get enough to to pay for GPS app at all airports - I'm speaking of course of pre-glass airline pilots. Nobody like shooting those NDB approaches in the sim. To say the NDB is a non-precision approach is an understatement - it's an emergency proceedure

It seems there is so much room for error shooting such an approach.

If you are simply renting an airplane to build time, not undergoing instruction, it is a bit of a strange policy. Presumably you have demonstrated your pilotage skills when you took your checkride and/or checkout. So now that you are simply renting, how you navigate, be it ipad, pilotage, kentucky windage, whatever, is basically your business IMHO provided it is done competently. Essentially I would be expecting to be treated like a grownup, otherwise I would look for somewhere a little less rigid to build time.

That said, plotting courses on paper and such is good practice and will make you a better pilot. Plus it's more fun to look out the window and identify landmarks than to tap tap tap on your ipad. We have enough gee-whiz distractions in our life, enjoy the simple flying while you can.

There are countries in the world other than the US.

This. I worked with a Ukrainian pilot who a year ago was an airline FO in the Ukraine. The only approaches he had routinely flown were ILS and NDB approaches.