Gomer, mainly utilize the link that coyotejeff provided, but to add and help answer a few of your questions.
Do you need a hunting license?
yes you either need a general hunting license or furtaking license to actively participate in hunting coyotes. Your friend may accompany you if he does not participate in any way (make sure you understand what participate means.....basically he may sit and observe, not run a call, not do anything in any fashion which is deemed participating)
Is coyote hunting 365?
With a furtakers license you may hunt coyote 24/7/365
With a general hunting license, there are a few restrictions on times you may hunt coyote, such as during any deer season, bear season, or spring gobbler (for Spring Gobbler you must adhere to shot size for turkey) you must be legally hunting deer or bear, spring gobbler (and be in possession of a valid tag) to be able to hunt coyotes during daylight hunting hours.
Also during general firearms deer season or bear season, you must adhere to the Flo orange requirements of those seasons
Also the best place to find some answers such as these is on pages 12 and 74 of the Pa Hunting and Trapping digest that you get when purchasing your license.
Can I get the coyote mounted or turned into a rug?
Yep
Can I use electronic decoys/callers?
Yep
Can I use bait for coyotes?
Yep, but make sure no other furbearers are taken around the bait...its not legal for fox,coon and other such animals.
Are the rules the same for fox?
No, you must have a furbearers license to take a fox.
Bait may not be used for fox.
Fox may be hunted 24/7 with exceptions during certain seasons.
Also I recommend contacting the PGC directly and asking to speak to a Law Enforcement supervisor to get questions answer more directly and to understand them better.
Some things are very difficult to express in writing and sometimes are taken wrong.
Happy hunting!!!