TL;DR: The lack of recognition leads to a "corruption tax" paid by the citizens of an unrecognized territory. That's why the recognition is the key factor for any region.
Consider this (the US is just for example below):
Politically, the US is an ally of Spain, and many international treaties recognize the territorial integrity of Spain, in its existing borders. Hence, the US will not co-operate with any entity that undermines this integrity.
Economically, imagine that an US exporter/importer signs a deal with a company based in the independent Catalonia. A legal Spanish competitor would seek justice and be able to win the case in the court.
So, the direct answer to your question,
How does this affect for example, exports and imports from United States and the European Union to the region of Catalonia?
— There will be zero direct exports and imports in this case.
However, there will be indirect trade, just the way how ISIS trades oil via the corrupted proxies located in recognized countries. Most obviously, such trade assumes significant discounts (also called "corruption tax", CT).
In other words, if a recognized entity sells something for
$1, an unrecognized one would be able to sell the same good for
$1-CT so that, after being "legalized" through a chain of corrupted proxies who take CT as a premium, the item could be legally sold for
The same applies to import: an unrecognized entity would be able to buy something for
So, the people who live in an unrecognized country, will suffer by paying the corruption tax twice: both for import and export. This is the main disadvantage.
A country can also rely on its own resources. For instance, Juche, the official state ideology of North Korea, is based on self-sustenance, relying solely on its own resources, and denying the international trade.