Do I need permission from the manufacturers when using Arduino and other electronics (such as DC/DC voltage converters, LCD screen and other common electronics) for constructing a new device that I want to patent?
In my 30+ years of engineering with over 90 patents have never once asked permission from a component manufacturer before filing a patent. I can't imagine a reason for doing so.
Where you might need permission from a component manufacturer is with the actual manufacturing and sale of the patented device. Even this is unusual. However, if you use a component in a way it was not designed to be used, there could present a potential liability to the component manufacturer.
To supplement @EricS answer - no actual prototype is needed especially in what is called “the predictable arts”. Some arrangement of electronics is going to work in a very predictable way. In manufacturing a product you have a chance to infringe any number of patents, not particularly those of your component suppliers.