I am lucky with my birds. Most allow me to look in the nest at anytime frome eggs to chicks hatching. I try not to disturb mine alot. Usually check when I see alot of time being spent in the nest to see if any eggs hae been laid, then again when the first egg is laid, then once again around a week later to see how many eggs and if all is ok. Then I let the hen do her thing until it is close to hatching day.

Around hatching time, I check every day to make sure all chicks are ok.
I have read lots of different opinions on this from leave birds alone to check them. I just do what I feel the hen will allow me to do.
Last year I had 3 chicks die soon after hatching and the fourth unhatched egg I removed and put under another hen who had clear eggs, to see if it was a parent thing.
I removed the clear eggs and replaced them with the remaining egg. Later that day the egg hatched. I kept a close eye on that chick since her siblings died under their parents care.
Luckily I did keep a close eye on things as this chick developed splayed legs and would have been too far gone to repair if I had not kept up with my nosiness.
I am not sure what happened with the 3 chicks that died, if it was a parent thing, the weather or just a bad season as many other breeders here had last year with nest deaths. The parents have bred successfully in the past for the previous owner. I hadn't checked the chicks much either and am kicking myself for it as if I had, then those 3 might still be alive today.
Having said all this, I have been told of birds that do not like having their nests checked and will be quite stressed over it. Like I said, maybe I am just lucky with my birds.
With pulling of chicks from the nest, I don't have a set age limit. It depends on my time allowance for feeding etc. Plus I prefer the chicks to get as much of mums goodness as possible. Sometimes I don't pully till 3 weeks or even 4. My last IRN, 'Junior G', I pulled a few days before s/he was ready to fledge and so far this has been the best chick ever!! No bluffing stage, very gentle, super affectionate etc. Just the best bird. Not sure if it has anything to do with it but 'Junior' was an only child while all my other chicks have had siblings to compete with for food attention etc. All my others who I pulled between 3-4 weeks of age have gone through the bluffing stage and was quite challenging at times lol They have all had brothers and sisters so I am wondering if sibling rivalry has anything to do with trying to be dominant?
When I do pull chicks, I keep the same family all together in the brooder. I keep chicks together from other parents but seperate from other families, if that makes sense. lol
This is just what works for me and I try to "read" my birds as to what I can get away with and treat each one accordingly.
I am sure others will have opinions and experience to share as well.
Good luck with it all happy chickies! lol