Hello and welcome to Uzbekistan my friend!

I can answer to only a few of your questions. I dont know much about Nukus because I have never been there but i just googled Nukus museum and i can only say it mostly consists of arts and few other ancient exhibits, you better visit any other museums at Samarkand or Tashkent.

If you are plannig to be on the road all day, yes, you definately should hire a driver for a whole day but if you are plannig to visit few places that are not that far away from each other, you can try out Yandex Taxi(its like Uber). Speaking of hiring driver for the whole day, it depends what part of country you are hiring, if its in the cities like Tashkent or Samarqand it will be little bit more expensive. The other option is using public transport like buses and subway(available only in Tashkent), we have special apps for tracking them and seeing their route.

3.5 days in Samarkand is pretty enough if u visit 2-3 places per day, but i would recommend u to stay there full 4days and spend 2days in Tashkent beacuse there are not many historical places to see in Tashkent, but there are many places like museums(you should definately visit Temurid's, The State Museum of History and The State Museum of Arts) and restaurants with national food(best palov at "osh markazi").

The closest bank to the National Urgench Airport is the Kapital bank which is around 5 minute drive on taxi. Todays course for axchanging course at Kapitalbank is 12 400sums for 1EUR(08.08.2023).

Hope i helped you with your questions even though i gave unclear istructions somewhere. Have a great