Well, I'm also a bit of an introvert, and I've been to a few cons, so maybe I can answer some of your questions:
How easy or difficult is it to start talking with a random person you never met before and might never see again whom you know nothing about?
This depends on the convention. At a big con, like MFF or Anthrocon there are a lot more people, but they are usually already socializing in small groups with their own friends. You'll probably have the best luck by joining in on organized activities (board games, panels, etc), then trying to talk to other people who aren't already in a closed social group.
At smaller cons, I've noticed that people are a lot more willing to strike up random conversations if you just hang out near tables, food, or general points of interest in the convention area. However, the most difficult part is actually making a connection beyond casual smalltalk. Either way, try to ask people questions about themselves that let them share something personal. For example, people *love* to talk in great detail about their fursonas at a furry convention!
When you're done talking, you really need to exchange contact info or plan to meet later, especially at big cons. I still find this whole process to be much more difficult than making friends online, but once you get each other's contact you can move it into that space.
Is there anyone else out there who was like me but was able to open up at a con? Stories hopefully?
Myself. I went to MFF last year, and I had a lot of trouble finding out how to talk to people; everyone seemed like they were just hanging out with their friend-groups and I was not sure how to approach. So, I decided to challenge myself to take photos with as many vulpine fursuiters as I could. That helped me talk to people in the lobby. However, the best solution turned out to be the game room. I enjoy playing Magic the Gathering, so I brought some cards with me. Pretty soon, I was meeting other furries who wanted to hang out and talk whilst playing MTG. Honestly, most of the time we didn't even play much, just talked.
How easy is it to find others who are willing to take in a guy like me who essentially doesn't talk, doesn't know meanings of some stuff, and automatically tries to hide?
There are definitely people who are willing; the hardest part is getting through the initial challenges of establishing a friendship.