Should you ideally be playing till your fingers hurt?
I want to keep playing till this happens but I always come short because of my wrist getting uncomfortable. I can only play a couple minutes before it gets uncomfortable.
It's not unusual for your finger tips to hurt as a beginner, BUT your wrist shouldn't. It sounds like you need to review your posture, etc. to get your wrist into a position where it's comfortable. You may develop serious problems if you don't.
Common beginner issues that seem to come up regularly here are:
1) Tilting the guitar towards you to see the fingerboard which puts pressure on your wrist as it has to bend through the extra angle;
2) Playing on a sofa or a low chair, or an office chair with arms etc. that means you can't adopt a correct seated position;
3) Having the neck of the guitar too low - go as far as having your fretting hand level with your ear!
If you're doing any of these things, try and correct it and get your wrist into a more natural position where it doesn't get uncomfortable.
Once you've developed a bit of technique you can probably compromise on any / all of these things because you will have learnt what doing it right feels like, and can make your own judgement.
I'm not sure what you hope to gain by the twisting exercise - it would concern me that it will do more harm than good.
Seriously - resolve the wrist issue. If you want to post a picture of you in playing position, we may be able to give you some pointers.
Andy