Can genetic engineering explain Peter Parker's / Spiderman's origins?

Spiderman has spider strength, spider strength and web shooting... and the ability to defy gravity!  How does Spiderman's powers hold up to scientific fact?  Which ones can be scientifically backed up, and which ones are pure science fiction?

Peter Parker gained his abilities after getting bit by a radioactive spider.  How much of this origin story could really happen?  Start the first video below at 3:40 to find out.

1. If an irradiated spider bites a person, will it transfer its radiation to the human?  
2. How might it be explained by genetic engineering?  

 

1. Transferring traits from one organism to another at the stage of inception is one things but...  is it possible to genetically modify a nearly grown man like Peter Parker?  The answer might be found in retroviruses (such as HIV) 
2. How could the genetic information passed along also help Peter Parker climb walls, shoot webs, and have the proportional strength of a spider?   (Beginning of video through 3:30)