Thank you for your query.
It is very common for children to have upper respiratory tract
infection 4-6 times and even more from 1 till about 5-6 years of age as they are developing their immunity. Removal of tonsils and adenoids
will not reduce this frequency.
The dark circles
under the eyes do not have anything to do with the removal of tonsils and adenoids. If your nephew is gaining weight adequately and growing as per the growth chart
then you need not worry about his appetite. Children do have their whims and fancies and even mood swings. We should not worry for it unless they are not growing as per the standards.
I hope I have answered your query to your satisfaction.
Wishing your nephew all the best.