Can hemorrhoids (external or internal) cause problems with urination? such as feeling like not emptying, and a pressure in the rectum?

Possible: Anatomically badder and rectum are close to each other to some extent. Having said that it s also possible the symptoms could be independent of each other. Only way to distinguish is to get checked and treated.

Yes and yes to both: The questions, as infected or inflamed hemorrhoids can affect the neighboring structures, like the urinary bladder/urthera or the rectum, with the symptoms you have mentioned. See a surgeon or a gastroenterologist, to be treated after properly diagnosed. Good luck.