Your display is 3.3V
You can quote as many Ebay vendors as you like. I can probably find an equivalent number of "green cheese" advocates.
Yes, your construction method is an excellent way to make a mechanically reliable project.
And it is very easy to mount series resistors or voltage dividers.
If you had placed the Nano on one side of your protoboard, you could have mounted a purpose level shifter i.c.
You might have damaged the ILI9341 with 5V logic. But it may have survived.
Please let us know how you get on (after you have added resistors or i.c.).
David.