Can Duonase help in treating nasal turbinate hypertrophy and nasal polyps? Is duonase similar to Nasonex (mometasone)?

It may help. Topical nasal steroids may help your problem. They are all about the same. There is little difference between the efficacy and safety of Flonase and nasonex (mometasone). I do not think turbinate hypertrophy will be much effected unless you have nasal allergy. Nasal polyposis will be more effectively treated with oral steroids.
Possibly. Duonase is a combo topical antihistamine and nasal steroid, hence "duo." It is certainly helpful for enlarged turbinates due to allergy. Also nasal steroids are used routine for nasal polyps. However, polyps really should be managed under ENT care. They often require oral steroid burst treatment and/or surgical removal. Also consider Singulair (montelukast) and allergy testing.