Are these LEGO pieces original? How can I be sure? When I enter in the code on the BrickLink site the codes come up, but there are no markings on the tires suggesting the name of the company or any code. Could it still be an original piece if this is the case?
For the rim I would say its original. 


LEGO made this part in Transparent. 
It has the correct mound ID 88517
And contains the LEGO logo + copyright symbol


Only this part comes in 2 sets which doesn't contain a tire.

The tire you have looks like Motorcycle Tyre Ø 100,6. Based on photos I cannot see any visible markings on the outside of the tire. I do own a couple of these tires myself but don't have access to them at the moment. So I can't check if there are any markings on the inside of the tire. 

If I check for example the Bugatti or the Harley-Davidson tire, all the id stuff that is not mentioned on the outside, is on the inside. See picture below of the small tire used in the Harley-Davidson.

So you can check the inside for any markings telling you if its an original part or not.