Is it advisable/ok to pull 2-3 frames of brood/eggs from two hives and introduce purchased queen?
a good way to make a strong split or nuc is to take frames from several hives and introduce a queen. You get a stronger nuc/split and it doesn't weaken the other hives to any great extent. In June I'll be taking a frame from each of my 5 hives and making a walkaway split that will still have time to raise a queen, lay several rounds of brood, and build up enough to overwinter in 2-3 medium boxes. Mixing frames from multiple hives creates confusion, and since brood frames are being used, by the time it gets sorted out it all just one happy hive.
If done in spring, I already have done 1 such split, you'll get harvest the 1st year and possibly avoid a swarm.
If done twice a year, spring and summer, you can build up strong hives each time. If you have 10 double deep, or equivalent, hives and you take 2 frames of brood from each hive you can make 2-3 strong splits in the spring, then in the summer, you now have 12-13 hives, and you repeat the process, you have 16-17 strong overwinterable hives come October. It is a good way to do a consistant buildup of strong hives or earn extra dollars selling off your excess.